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Quantum state transfer is one of the basic tasks in quantum information processing. We here propose a theoretical approach to realize arbitrary entangled state transfer through a qubit chain, which is a class of extended Su-Schrieffer-Heeger models and accommodates multiple topological edge states separated from the bulk states. We show that an arbitrary entangled state, from $2$-qubit to $\mathcal{N}$-qubit, can be encoded in the corresponding edge states, and then adiabatically transferred from one end to the other of the chain. The dynamical phase differences resulting from the time evolutions of different edge states can be eliminated by properly choosing evolution time. Our approach is robust against both the qubit-qubit coupling disorder and the evolution time disorder. For the concreteness of discussions, we assume that such a chain is constructed by an experimentally feasible superconducting qubit system, meanwhile, our proposal can also be applied to other systems.

Over the last decade, quantum computing has experienced significant changes and captured worldwide attention. In particular, superconducting qubits have become the leading candidates for scalable quantum computers, and a number of cryogenic materials have scientifically demonstrated their potential uses in constructing qubit chips. However, because of insufficient coherence time, establishing a robust and scalable quantum platform is still a long-term goal. Another consideration is the control circuits essential to initializing, operating and measuring the qubits. To keep noise low, control circuits in close proximity to the qubits require superior reliability in the cryogenic environment. The realization of the quantum advantage demands qubits with appropriate circuitry designs to maintain long coherence times and entanglement. In this work, we briefly summarize the current status of cryogenic materials for qubits and discuss typical cryogenic circuitry designs and integration techniques for qubit chips. In the end, we provide an assessment of the prospects of quantum computers and some other promising cryogenic materials.

We propose an implementation of a generalized Su-Schrieffer-Heeger (SSH) model based on optomechanical arrays. The topological properties of the generalized SSH model depend on the effective optomechanical interactions enhanced by strong driving optical fields. Three phases including one trivial and two distinct topological phases are found in the generalized SSH model. The phase transition can be observed by turning the strengths and phases of the effective optomechanical interactions via adjusting the external driving fields. Moreover, four types of edge states can be created in generalized SSH model of an open chain under single-particle excitation, and the dynamical behaviors of the excitation in the open chain are related to the topological properties under the periodic boundary condition. We show that the edge states can be pumped adiabatically along the optomechanical arrays by periodically modulating the amplitude and frequency of the driving fields. The generalized SSH model based on the optomechanical arrays provides us a tunable platform to engineer topological phases for photons and phonons, which may have potential applications in controlling the transport of photons and phonons., Comment: 11 pages, 14 figures

The interaction between the quantum emitter and topological photonic system makes both the emitter and the photon behave in exotic ways. We here study a system that a giant atom is coupled to two points of a one-dimensional topological waveguide formed by the Su-Schrieffer-Heeger (SSH) chain. The topological nature of the hybrid system is studied. We find that the giant atom can act as an effective boundary and induce the chiral zero energy modes for the waveguide under the periodical boundary. The properties of these modes are similar to those in the SSH model with open boundary. Meanwhile, the SSH waveguide, as a structured environment, induces the retarded effect and the non-Markovian dissipation of the giant atom. Our work may promote more studies on the interaction between matter and topological environment. Experimental demonstration for our study using superconducting quantum circuits is very possible within current technology., 21 Pages, 20 Figures

We study the phase controlled transmission properties in a compound system consisting of a 3D copper cavity and an yttrium iron garnet (YIG) sphere. By tuning the relative phase of the magnon pumping and cavity probe tones, constructive and destructive interferences occur periodically, which strongly modify both the cavity field transmission spectra and the group delay of light. Moreover, the tunable amplitude ratio between pump-probe tones allows us to further improve the signal absorption or amplification, accompanied by either significantly enhanced optical advance or delay. Both the phase and amplitude-ratio can be used to realize in-situ tunable and switchable fast-slow light. The tunable phase and amplitude-ratio lead to the zero reflection of the transmitted light and an abrupt fast-slow light transition. Our results confirm that direct magnon pumping through the coupling loops provides a versatile route to achieve controllable signal transmission, storage, and communication, which can be further expanded to the quantum regime, realizing coherent-state processing or quantum-limited precise measurements., Comment: 24 pages, 5 figures

We propose to periodically modulate the onsite energy via two-tone drives, which can be furthermore used to engineer artificial gauge potential. As an example, we show that the fermionic ladder model penetrated with effective magnetic flux can be constructed by superconducting flux qubits using such two-tone-drive-engineered artificial gauge potential. In this superconducting system, the single-particle ground state can range from vortex phase to Meissner phase due to the competition between the interleg coupling strength and the effective magnetic flux. We also present the method to experimentally measure the chiral currents by the single-particle Rabi oscillations between adjacent qubits. In contrast to previous methods of generating artifical gauge potential, our proposal does not need the aid of auxiliary couplers and in principle remains valid only if the qubit circuit maintains enough anharmonicity. The fermionic ladder model with effective magnetic flux can also be interpreted as one-dimensional spin-orbit-coupled model, which thus lay a foundation towards the realization of quantum spin Hall effect.

Toward quantum machine learning deployed on imperfect near-term intermediate-scale quantum (NISQ) processors, the entire physical implementation of should include as less as possible hand-designed modules with only a few ad-hoc parameters to be determined. This work presents such a hardware-friendly end-to-end quantum machine learning scheme that can be implemented with imperfect near-term intermediate-scale quantum (NISQ) processors. The proposal transforms the machine learning task to the optimization of controlled quantum dynamics, in which the learning model is parameterized by experimentally tunable control variables. Our design also enables automated feature selection by encoding the raw input to quantum states through agent control variables. Comparing with the gate-based parameterized quantum circuits, the proposed end-to-end quantum learning model is easy to implement as there are only few ad-hoc parameters to be determined. Numerical simulations on the benchmarking MNIST dataset demonstrate that the model can achieve high performance using only 3-5 qubits without downsizing the dataset, which shows great potential for accomplishing large-scale real-world learning tasks on NISQ processors.arning models. The scheme is promising for efficiently performing large-scale real-world learning tasks using intermediate-scale quantum processors., Comment: 10 pages, 6 figures

Topological matter and topological optics have been studied in many systems, with promising applications in materials science and photonics technology. These advances motivate the study of the interaction between topological matter and light, as well as topological protection in light-matter interactions. In this work, we study a waveguide-interfaced topological atom array. The light-matter interaction is nontrivially modified by topology, yielding novel optical phenomena. We find topology-enhanced photon absorption from the waveguide for large Purcell factor, i.e., $\Gamma/\Gamma_0\gg 1$, where $\Gamma$ and $\Gamma_0$ are the atomic decays to waveguide and environment, respectively. To understand this unconventional photon absorption, we propose a multi-channel scattering approach and study the interaction spectra for edge- and bulk-state channels. We find that, by breaking inversion and time-reversal symmetries, optical anisotropy is enabled for reflection process, but the transmission is isotropic. Through a perturbation analysis of the edge-state channel, we show that the anisotropy in the reflection process originates from the waveguide-mediated non-Hermitian interaction. However, the inversion symmetry in the non-Hermitian interaction makes the transmission isotropic. At a topology-protected atomic spacing, the subradiant edge state exhibits huge anisotropy. Due to the interplay between edge- and bulk-state channels, a large topological bandgap enhances nonreciprocal reflection of photons in the waveguide for weakly broken time-reversal symmetry, i.e., $\Gamma_0/\Gamma\ll 1$, producing complete photon absorption. We show that our proposal can be implemented in superconducting quantum circuits. The topology-enhanced photon absorption is useful for quantum detection. This work shows the potential to manipulate light with topological quantum matter., Comment: 15 pages, 8 figures

We study the absorption spectrum of a probe field by a Λ-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler-Townes splitting (ATS). We also find that the parameter changing from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization.

We experimentally study a circuit quantum acoustodynamics system, which consists of a superconducting artificial atom, coupled to both a two-dimensional surface acoustic wave resonator and a one-dimensional microwave transmission line. The strong coupling between the artificial atom and the acoustic wave resonator is confirmed by the observation of the vacuum Rabi splitting at the base temperature of dilution refrigerator. We show that the propagation of microwave photons in the microwave transmission line can be controlled by a few phonons in the acoustic wave resonator. Furthermore, we demonstrate the temperature effect on the measurements of the Rabi splitting and temperature induced transitions from high excited dressed states. We find that the spectrum structure of two-peak for the Rabi splitting becomes into those of several peaks, and gradually disappears with the increase of the environmental temperature $T$. The quantum-to-classical transition is observed around the crossover temperature $T_{c}$, which is determined via the thermal fluctuation energy $k_{B}T$ and the characteristic energy level spacing of the coupled system. Experimental results agree well with the theoretical simulations via the master equation of the coupled system at different effective temperatures., Comment: 14 pages, 6 figures

Synchronization has great impacts in various fields such as self-clocking, communication, and neural networks. Here, we present a mechanism of synchronization for two mechanical modes in two coupled optomechanical resonators with a parity-time ( PT )-symmetric structure. It is shown that the degree of synchronization between the two far-off-resonant mechanical modes can be increased by decreasing the coupling strength between the two optomechanical resonators due to the large amplification of optomechanical interaction near the exceptional point. Additionally, when we consider the stochastic noises in the optomechanical resonators by working near the exceptional point, we find that more noises can enhance the degree of synchronization of the system under a particular parameter regime. Our results open up a new dimension of research for PT -symmetric systems and synchronization.

We study the controllable single-photon scattering via a one-dimensional waveguide which is coupled to a two-level emitter and a single-mode cavity simultaneously. The emitter and the cavity are also coupled to each other and form a three-level system with cyclic transitions within the zero- and single-excitation subspaces. As a result, the phase of emitter-cavity coupling strength serves as a sensitive control parameter. When the emitter and cavity locate at the same point of the waveguide, we demonstrate the Rabi splitting and quasidark-state--induced perfect transmission for the incident photons. More interestingly, when they locate at different points of the waveguide, a controllable nonreciprocal transmission can be realized and the non-reciprocity is robust to the weak coupling between the system and environment. Furthermore, we demonstrate that our theoretical model is experimentally feasible with currently available technologies., 11 pages, 8 figures,Accepted by Phys. Rev. A

Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.

Stimulated emission and absorption are two fundamental processes of light-matter interaction, and the coefficients of the two processes should be equal in general. However, we will describe a generic method to realize significant difference between the stimulated emission and absorption coefficients of two nondegenerate energy levels, which we refer to as nonreciprocal transition. As a simple implementation, a cyclic three-level atom system, comprising two nondegenerate energy levels and one auxiliary energy level, is employed to show nonreciprocal transition via a combination of synthetic magnetism and reservoir engineering. Moreover, a single-photon nonreciprocal transporter is proposed using two one dimensional semi-infinite coupled-resonator waveguides connected by an atom with nonreciprocal transition effect. Our work opens up a route to design atom-mediated nonreciprocal devices in a wide range of physical systems., 6 pages + Supplemental Materials (6 pages), 5 figures

We study photon, phonon statistics and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade and strongly anticorrelated photons and phonons can be observed in the same parameter regime with the effective nonlinear coupling between the optical and mechanical modes, enhanced by a strong optical driving field. Interestingly, an optimal value of the effective nonlinear coupling strength for the photon blockade is not within the strong nonlinear coupling regime. This abnormal phenomenon results from the destructive interference between different paths for two-photon excitation in the optical mode with a moderate effective nonlinear coupling strength. Further more, we show that phonon (photon) pairs and correlated photons and phonons can be generated in the strong nonlinear coupling regime with a proper detuning between the weak mechanical driving field and mechanical mode. Our results open up a way to generate anticorrelated and correlated photons and phonons, which may have important applications in quantum information processing., 9 pages, 6 figures

By simultaneously coupling multiple two-level artificial atoms to two superconducting resonators, we design a quantum switch that tunes the resonator-resonator coupling strength from zero to a large value proportional to the number of qubits. This process is implemented by engineering the qubits into different subradiant states, where the microwave photons decay from different qubits destructively interfere with each other such that the resonator-resonator coupling strength keeps stable in an open environment. Based on a three-step control scheme, we switch the coupling strength among different values within nanoseconds without changing the transition frequency of the qubits. We also apply the quantum switch to a network of superconducting resonators, and demonstrate its potential applications in quantum simulation and quantum information storage and processing.

We present an approach to achieve efficient single-photon frequency conversion in the microwave domain based on coherent control in superconducting quantum circuits, which consist of a driven artificial atom coupled to a semi-infinite transmission line. Using the full quantum-mechanical method, we analyze the single-photon scattering process in this system and find that single-photon frequency up- or down-conversion with efficiency close to unity can be achieved by adjusting the parameters of the control field applied to the artificial atom. We further show that our approach is experimentally feasible in currently available superconducting flux qubit circuits., 14 pages, 8 figures

We propose to construct a nonreciprocal single-photon frequency converter via multiple semi-infinite coupled-resonator waveguides (CRWs). We first demonstrate that the frequency of a single photon can be converted nonreciprocally through two CRWs, which are coupled indirectly by optomechanical interactions with two nondegenerate mechanical modes. Based on such nonreciprocity, two different single-photon circulators are proposed in the T-shaped waveguides consisting of three semi-infinite CRWs, which are coupled in pairwise by optomechanical interactions. One circulator is proposed by using two nondegenerate mechanical modes and the other one is proposed by using three nondegenerate mechanical modes. Nonreciprocal single-photon frequency conversion is induced by breaking the time-reversal symmetry, and the optimal conditions for nonreciprocal frequency conversion are obtained. These proposals can be used to realize nonreciprocal frequency conversion of single photons in any two distinctive waveguides with different frequencies and they can allow for dynamic control of the direction of frequency conversion by tuning the phases of external driving lasers, which may have versatile applications in hybrid quantum networks., 13 pages, 10 figures. arXiv admin note: text overlap with arXiv:1703.03969

We propose a bosonic Josephson junction (BJJ) in two nonlinear mechanical resonator coupled through two-phonon exchange interaction induced by quadratic optomechanical couplings. The nonlinear dynamic equations and effective Hamiltonian are derived to describe behaviors of the BJJ. We show that the BJJ can work in two different dynamical regimes: Josephson oscillation and macroscopic self-trapping. The system can transfer from one regime to the other one when the self-interaction and asymmetric parameters exceed their critical values. We predict that a transition from Josephson oscillation to macroscopic self-trapping can be induced by the phonon damping in the asymmetric BJJs. Our results opens up a way to demonstrate BJJ with two-phonon exchange interaction and can be applied to other systems, such as the optical and microwave systems., Comment: 7 pages, 7 figures

In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field., Review article, 170 pages (main text 101 pages), 35 figures, 5 tables, 1362 references; v2: a few more references added, typos corrected; Physics Reports (in press)

We study the transport of a single photon in two coupled one-dimensional semi-infinite coupled-resonator waveguides (CRWs), in which both end sides are coupled to a dissipative cavity. We demonstrate that a single photon can transfer from one semi-infinite CRW to the other nonreciprocally. Based on such nonreciprocity, we further construct a three-port single-photon circulator by a T-shaped waveguide, in which three semi-infinite CRWs are pairwise mutually coupled to each other. The single-photon nonreciprocal transport is induced by the breaking of the time-reversal symmetry and the optimal conditions for these phenomena are obtained analytically. The CRWs with broken time-reversal symmetry will open up a kind of quantum devices with versatile applications in quantum networks., 10 pages, 6 figures

We experimentally study a vacuum-induced Autler-Townes doublet in a superconducting three-level artificial atom strongly coupled to a coplanar waveguide resonator and simultaneously to a transmission line. The Autler-Townes splitting is observed in the reflection spectrum from the three-level atom in a transition between the ground state and the second excited state when the transition between the two excited states is resonant with a resonator. By applying a driving field to the resonator, we observe a change in the regime of the Autler-Townes splitting from quantum (vacuum-induced) to classical (with many resonator photons). Furthermore, we show that the reflection of propagating microwaves in a transmission line could be controlled by different frequency single photons in a resonator., Comment: 5 pages, 3 figures+supplementary materials

We theoretically study a strongly driven optomechanical system which consists of a passive optical cavity and an active mechanical resonator. When the optomechanical coupling strength is varied, phase transitions, which are similar to those observed in $\mathcal{PT}$-symmetric systems, are observed. We show that the optical transmission can be controlled by changing the gain of the mechanical resonator and loss of the optical cavity mode. Especially, we find that (i) for balanced gain and loss, optical amplification and absorption can be tuned by changing the optomechanical coupling strength through a control field; (ii) for unbalanced gain and loss, even with a tiny mechanical gain, both optomechanically induced transparency and anomalous dispersion can be observed around a critical point, which exhibits an ultralong group delay. The time delay $\ensuremath{\tau}$ can be optimized by regulating the optomechanical coupling strength through the control field, and it can be improved up to several orders of magnitude ($\ensuremath{\tau}\ensuremath{\sim}2\phantom{\rule{4pt}{0ex}}\mathrm{ms}$) compared to that of conventional optomechanical systems ($\ensuremath{\tau}\ensuremath{\sim}1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$). The presence of mechanical gain makes the group delay more robust to environmental perturbations. Our proposal provides a powerful platform to control light transport using a $\mathcal{PT}$-symmetric-like optomechanical system.

We study phonon statistics in a nanomechanical resonator (NAMR) which is resonantly coupled to a qubit. We find that there are two different mechanisms for phonon blockade in such a resonantly coupled NAMR-qubit system. One is due to the strong anharmonicity of the NAMR-qubit system with large coupling strength; the other one is due to the destructive interference between different paths for two-phonon excitation in the NAMR-qubit system with a moderate coupling strength. We find that the phonon blockade is fragile towards thermal mode occupations and can only be observed for NAMR being at ultracold effective temperature. In order to enlarge the mean phonon number for strong phonon antibunching with a moderate NAMR-qubit coupling strength, we assume that two external driving fields are applied to the NAMR and qubit, respectively. In this case, we find that the phonon blockades under two mechanisms can appear at the same frequency regime by optimizing the strength ratio and phase difference of the two external driving fields., 11 pages, 11 figures

Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. Fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices., 12 papges and 16 figures

Electromagnetically induced transparency (EIT) has been extensively studied in various systems. However, it is not easy to observe in superconducting quantum circuits (SQCs), because the Rabi frequency of the strong controlling field corresponding to EIT is limited by the decay rates of the SQCs. Here, we show that EIT can be achieved by engineering decay rates in a superconducting circuit QED system through a classical driving field on the qubit. Without such a driving field, the superconducting qubit and the cavity field are approximately decoupled in the large detuning regime, and thus the eigenstates of the system are approximately product states of the cavity field and qubit states. However, the driving field can strongly mix these product states and so-called polariton states can be formed. The weights of the states for the qubit and cavity field in the polariton states can be tuned by the driving field, and thus the decay rates of the polariton states can be changed. We choose a three-level system with $\Lambda$-type transitions in such a driven circuit QED system, and demonstrate how EIT and ATS can be realized in this compound system. We believe that this study will be helpful for EIT experiments using SQCs., Comment: 12 pages, 8 figures

It has been shown that there are not only transverse but also longitudinal couplings between microwave fields and a superconducting qubit with broken inversion symmetry of the potential energy. Using multiphoton processes induced by longitudinal coupling fields and frequency matching conditions, we design a universal algorithm to produce arbitrary superpositions of two-mode photon states of microwave fields in two separated transmission line resonators, which are coupled to a superconducting qubit. Based on our algorithm, we analyze the generation of evenly-populated states and NOON states. Compared to other proposals with only single-photon process, we provide an efficient way to produce entangled microwave photon states when the interactions between superconducting qubits and microwave fields are in the strong and ultrastrong regime.

When a gain system is coupled to a loss system, the energy usually flows from the gain system to the loss one. We here present a counterintuitive theory for the ground-state cooling of the mechanical resonator in optomechanical system via a gain cavity. The energy flows first from the mechanical resonator into the loss cavity, then into the gain cavity, and finally localizes there. The energy localization in the gain cavity dramatically enhances the cooling rate of the mechanical resonator. Moreover, we show that unconventional optical spring effect, e.g., giant frequency shift and optically induced damping of the mechanical resonator, can be realized. Those feature a pre-cooling free ground-state cooling, i.e., the mechanical resonator in thermal excitation at room temperature can directly be cooled to its ground state. This cooling approach has the potential application for fundamental tests of quantum physics without complicated cryogenic setups., Comment: 15 pages, 6 figures

Using different configurations of applied strong driving and weak probe fields, we find that only a single three-level superconducting quantum circuit (SQC) is enough to realize amplification, attenuation, and frequency conversion of microwave fields. Such a three-level SQC has to possess $\mathrm{\ensuremath{\Delta}}$-type cyclic transitions. Different from the parametric amplification (attenuation) and frequency conversion in nonlinear optical media, the real energy levels of the three-level SQC are involved in the energy exchange when these processes are completed. We quantitatively discuss the effects of amplification (attenuation) and the frequency conversion for different types of driving fields. The values and conditions are obtained for the optimal gains for amplification (attenuation) and the optimal conversion efficiencies. Our study provides a method to amplify (attenuate) microwave, realize frequency conversion, and also lay a foundation for generating single or entangled microwave photon states using a single three-level SQC.

We propose a method to decouple the nanomechanical resonator in optomechanical systems from the environmental noise by introducing a chaotic coherent feedback loop. We find that the chaotic controller in the feedback loop can modulate the dynamics of the controlled optomechanical system and induce a broadband response of the mechanical mode. This broadband response of the mechanical mode will cut off the coupling between the mechanical mode and the environment and thus suppress the environmental noise of the mechanical modes. As an application, we use the protected optomechanical system to act as a quantum memory. It is shown that the noise-decoupled optomechanical quantum memory is efficient for storing information transferred from coherent or squeezed light.

We present a method for quantum entanglement distribution over a so-called code-division-multiple-access network, in which two pairs of users share the same quantum channel to transmit information. The main idea of this method is to use different broad-band chaotic phase shifts, generated by electro-optic modulators (EOMs) and chaotic Colpitts circuits, to encode the information-bearing quantum signals coming from different users, and then recover the masked quantum signals at the receiver side by imposing opposite chaotic phase shifts. The chaotic phase shifts given to different pairs of users are almost uncorrelated due to the randomness of chaos and thus the quantum signals from different pair of users can be distinguished even when they are sent via the same quantum channel. It is shown that two maximally-entangled states can be generated between two pairs of users by our method mediated by bright coherent lights, which can be more easily implemented in experiments compared with single-photon lights. Our method is robust under the channel noises if only the decay rates of the information-bearing fields induced by the channel noises are not quite high. Our study opens up new perspectives for addressing and transmitting quantum information in future quantum networks.

A single phonon in a nonlinear nanomechanical resonator (NAMR) can block the excitation of a second phonon [Phys. Rev. A 82, 032101 (2010)]. This intrinsically quantum effect is called phonon blockade, and is an analog of Coulomb blockade and photon blockade. Here we predict tunable multiphonon blockade in coupled nonlinear NAMRs, where nonlinearity is induced by two-level systems (TLSs) assuming dispersive (far off-resonance) interactions. Specifically, we derive an effective Kerr-type interaction in a hybrid system consisting of two nonlinearly-interacting NAMRs coupled to two TLSs and driven by classical fields. The interaction between a given NAMR and a TLS is described by a Jaynes-Cummings-like model. We show that by properly tuning the frequency of the driving fields one can induce various types of phonon blockade, corresponding to the entangled phonon states of either two qubits, qutrit and quartit, or two qudits. Thus, a $k$-phonon Fock state (with $k=1,2,3$) can impede the excitation of more phonons in a given NAMR, which we interpret as a $k$-phonon blockade (or, equivalently, phonon tunneling). Our results can be explained in terms of resonant transitions in the Fock space and via phase-space interference using the $s$-parametrized Cahill-Glauber quasiprobability distributions including the Wigner function. We study the nonclassicality, entanglement, and dimensionality of the blockaded phonon states during both dynamics and in the stationary limits., 15 pages, 14 figures, to appear in PRA

We study the effect of mode-coupling on a single-photon device in which a dipole-quantum-emitter (DQE) is embedded in a bimodal whispering-gallery-mode cavity (WGMC). A scatterer is used to induce mode coupling between counter-clockwise and clockwise propagating light fields, which interact with the DQE. In contrast to models for the interaction between a DQE and a (one-mode or two-mode) cavity field, we find that strong photon antibunching can occur even for a weak DQE-field coupling and large dephasing of the DQE, when mode coupling is introduced. We also find that mode coupling can make the device robust against either the frequency mismatch between cavity modes and the DQE or the coupling strength mismatch between the DQE and each mode in the two-mode cavity. Moreover, we find that these mismatches can be used to generate better antibunching in the weak DQE-field coupling regime. Our study shows that mode coupling in a bimodal cavity is very important for the realization of a good single-photon device., 12pages,11figures

We study photon blockade and anti-bunching in the cavity of an optomechanical system in which the mechanical resonator is coupled to a two-level system (TLS). In particular, we analyze the effects of the coupling strength (to the mechanical mode), transition frequency, and decay rate of TLS on the photon blockade. The statistical properties of the cavity field are affected by the TLS, because the TLS changes the energy-level structure of the optomechanical system via dressed states formed by the TLS and the mechanical resonator. We find that the photon blockade and tunneling can be significantly changed by the transition frequency of the TLS and the coupling strength between the TLS and the mechanical resonator. Therefore, our study provides a method to tune the photon blockade and tunneling using a controllable TLS., 11 pages

Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these classical-field-assisted multiphoton processes of the single-mode cavity field are very similar to those for cold ions, confined to a coaxial RF-ion trap and driven by a classical field. We show that arbitrary superpositions of Fock states can be more efficiently generated using these controllable multiphoton transitions, in contrast to the single-photon resonant transition when there is only a SQ-field transverse coupling. The experimental feasibility for different SQs is also discussed., 15 pages, 8 figures

A single superconducting artificial atom provides a unique basis for coupling electromagnetic fields and photons hardly achieved with a natural atom. Bringing a pair of harmonic oscillators into resonance with transitions of the three-level atom converts atomic spontaneous processes into correlated emission dynamics. We demonstrate two-mode correlated emission lasing on harmonic oscillators coupled via the fully controllable three-level artificial atom. Correlation of two different color emissions reveals itself as equally narrowed linewiths and quench of their mutual phase-diffusion. The mutual linewidth is more than four orders of magnitude narrower than the Schawlow-Townes limit. The interference between the different color lasing fields demonstrates the two-mode fields are strongly correlated., Comment: 5 pages, 4 figures + supplemenntary materials accepted for publication in Phys. Rev. Lett

We propose to demonstrate nonreciprocal conversion between microwave and optical photons in an electro-optomechanical system where a microwave mode and an optical mode are coupled indirectly via two non-degenerate mechanical modes. The nonreciprocal conversion is obtained in the broken time-reversal symmetry regime, where the conversion of photons from one frequency to the other is enhanced for constructive quantum interference while the conversion in the reversal direction is suppressed due to destructive quantum interference. It is interesting that the nonreciprocal response between the microwave and optical modes in the electro-optomechanical system appears at two different frequencies with opposite directions. The proposal can be used to realize nonreciprocal conversion between photons of any two distinctive modes with different frequencies. Moreover, the electro-optomechanical system can also be used to construct a three-port circulator for three optical modes with distinctively different frequencies by adding an auxiliary optical mode coupled to one of the mechanical modes., Comment: 10 pages, 4 figures

Josephson qubits without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an oscillator with adjustable frequency. The coupling between any qubit and the bus can be controlled by modulating the magnetic flux applied to that qubit. This tunable and selective coupling provides two-qubit entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality., Comment: 10 pages, 1 figure. submitted

We study a general theory of phonon lasing [I. S. Grudinin et al., Phys. Rev. Lett. 104, 083901 (2010)] in coupled optomechancial systems. We derive the dynamical equation of the phonon lasing using supermodes formed by two cavity modes. A general threshold condition for phonon lasing is obtained. We also show the differences between phonon lasing and photon lasing, generated by photonic supermodes and two-level atomic systems, respectively. We find that the phonon lasing can be realized in certain parameter regime near the threshold. The phase diagram and second-order correlation function of the phonon lasing are also studied to show some interesting phenomena that cannot be observed in the common photon lasing with the two-level systems., Comment: 11 pages, 8 figures

We explore theoretically the optical response properties in an optomechanical system under electromagneti- cally induced transparency condition but with the mechanical resonator being driven by an additional coherent field. In this configuration, more complex quantum coherent and interference phenomena occur. In partic- ular, we find that the probe transmission spectra depend on the total phase of the applied fields. Our study also provides an efficient way to control propagation of amplification., 8 pages, 5 figures

Some optomechanical systems can be transparent to a probe field when a strong driving field is applied. These systems can provide an optomechanical analogue of electromagnetically-induced transparency (EIT). We study the transmission of a probe field through a hybrid optomechanical system consisting of a cavity and a mechanical resonator with a two-level system (qubit). The qubit might be an intrinsic defect inside the mechanical resonator, a superconducting artificial atom, or another two-level system. The mechanical resonator is coupled to the cavity field via radiation pressure and to the qubit via the Jaynes-Cummings interaction. We find that the dressed two-level system and mechanical phonon can form two sets of three-level systems. Thus, there are two transparency windows in the discussed system. We interpret this effect as an optomechanical analog of two-color EIT (or double-EIT). We demonstrate how to switch between one and two EIT windows by changing the transition frequency of the qubit. We show that the absorption and dispersion of the system are mainly affected by the qubit-phonon coupling strength and the transition frequency of the qubit., Comment: 10 pages, 9 figures

An arbitrary initial state of an optical or microwave field in a lossy driven nonlinear cavity can be changed, in the steady-state limit, into a partially incoherent superposition of only the vacuum and the single-photon states. This effect is known as single-photon blockade, which is usually analyzed for a Kerr-type nonlinear cavity parametrically driven by a single-photon process assuming single-photon loss mechanisms. We study photon blockade engineering via a squeezed reservoir, i.e., a quantum reservoir, where only two-photon absorption is allowed. Namely, we analyze a lossy nonlinear cavity parametrically driven by a two-photon process and allowing two-photon loss mechanisms, as described by the master equation derived for a two-photon absorbing reservoir. The nonlinear cavity engineering can be realized by a linear cavity with a tunable two-level system via the Jaynes-Cummings interaction in the dispersive limit. We show that by tuning properly the frequencies of the driving field and the two-level system, the steady state of the cavity field can be the single-photon Fock state or a partially incoherent superposition of several Fock states with photon numbers, e.g., (0,2), (1,3), (0,1,2), or (0,2,4). We observe that an arbitrary initial coherent or incoherent superposition of Fock states with an even (odd) number of photons can be changed into a partially incoherent superposition of a few Fock states of the same photon-number parity. A general solution for an arbitrary initial state is a weighted mixture of the above two solutions with even and odd photon numbers, where the weights are given by the probabilities of measuring the even and odd numbers of photons of the initial cavity field, respectively. Thus, in contrast to the standard photon blockade, we prove that the steady state in the engineered photon blockade, can depend on its initial state., 16 pages, 15 figures, 1 table

We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximation, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The linear magnetic susceptibility of the SFQC can be changed by both the driving field and the bias magnetic flux. When the bias magnetic flux is at the optimal point, the transition from the ground state to the second excited state is forbidden and the three-level SFQC has a ladder-type transition. Thus, the SFQC responds to the probe field like natural atoms with ladder-type transitions. However, when the bias magnetic flux deviates from the optimal point, the three-level SFQC has a cyclic transition, thus it responds to the probe field like a combination of natural atoms with ladder-type transitions and natural atoms with $\Lambda$-type transitions. In particular, we provide detailed discussions on the conditions for realizing electromagnetically induced transparency and Autler-Townes splitting in three-level SFQCs., Comment: 20 pages, 8 figures

We propose to realize mechanical parity-time PT symmetry in two coupled optomechanical systems. To provide gain to one mechanical resonator and the same amount of damping to the other, the two optical cavities should be driven by blue- and red-detuned laser fields, respectively. After adiabatically eliminating the degrees of freedom of the cavity modes, we derive a formula to describe the PT symmetry of two coupled mechanical resonators. Mechanical PT-symmetric phase transition is demonstrated by the dynamical behavior of the mechanical resonators. Moreover, we study the effect of the quantum noises on the dynamical behavior of the mechanical resonators when the system is in the quantum regime., 12 pages, 11 figures

The control of individual quantum systems is now a reality in a variety of physical settings. Feedback control is an important class of control methods because of its ability to reduce the effects of noise. In this review we give an introductory overview of the various ways in which feedback may be implemented in quantum systems, the theoretical methods that are currently used to treat it, the experiments in which it has been demonstrated to-date, and its applications. In the last few years there has been rapid experimental progress in the ability to realize quantum measurement and control of mesoscopic systems. We expect that the next few years will see further rapid advances in the precision and sophistication of feedback control protocols realized in the laboratory., Comment: Updated version of a review paper about quantum feedback

We propose a method to generate entangled states of the vibrational modes of N membranes which are coupled to a cavity mode via the radiation pressure. Using sideband excitations, we show that arbitrary entangled states of vibrational modes of different membranes can be produced in principle by sequentially applying a series of classical pulses with desired frequencies, phases and durations. As examples, we show how to synthesize several typical entangled states, for example, Bell states, NOON states, GHZ states and W states. The environmental effect, information leakage, and experimental feasibility are briefly discussed. Our proposal can also be applied to other experimental setups of optomechanical systems, in which many mechanical resonators are coupled to a common sing-mode cavity field via the radiation pressure., 15 pages, 10 figures

In contrast to recent studies [Rabl, Phys. Rev. Lett. 107, 063601 (2011); Nunnenkamp et al., Phys. Rev. Lett. 107, 063602 (2011)] on photon blockade that prevents subsequent photons from resonantly entering the cavity in optomechanical systems, we study the photon-induced tunneling that increases the probability of admitting subsequent photons in those systems. In particular, we analytically and numerically show how twoor three-photon tunneling can occur by avoiding single-photon blockade. Our study provides another way on photon control using a single mechanical resonator in optomechanical systems., Comment: 5 pages, 4 figures

Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired by the recent progress of quantum feedback experiments, especially those in mesoscopic circuits, we prove that superconducting circuit QED systems, shunted with a coherent feedback loop, can change the dynamics of a superconducting transmission line resonator, i.e., a linear quantum cavity, and lead to strong on-chip nonlinear optical phenomena. We find that bistability can occur under the semiclassical approximation, and photon anti-bunching can be shown in the quantum regime. Our study presents new perspectives for engineering nonlinear quantum dynamics on a chip., Comment: 10 pages, 9 figures