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We study the multiple-photon bundle emission in the $n$-photon Jaynes-Cummings model composed of a two-level system coupled to a single-mode optical field via the $n$-photon exciting process. Here, the two-level system is strongly driven by a near-resonant monochromatic field, and hence the system can work in the Mollow regime, in which a super-Rabi oscillation between the zero-photon state and the $n$-photon state can take place under proper resonant conditions. We calculate the photon number populations and the standard equal-time high-order correlation functions, and find that the multiple-photon bundle emission can occur in this system. The multiple-photon bundle emission is also confirmed by investigating the quantum trajectories of the state populations and both the standard and generalized time-delay second-order correlation functions for multiple-photon bundle. Our work paves the way towards the study of multiple-photon quantum coherent devices, with potential application in quantum information sciences and technologies., 10 pages, 6 figures

Ground-state cooling of mechanical resonators is an important task in quantum optomechanics, because it is a necessary prerequisite for creation, manipulation, and application of macroscopic mechanical coherence. Here, we propose a transient-state scheme to accelerate ground-state cooling of a mechanical resonator in a three-mode loop-coupled optomechanical system via shortcuts to adiabaticity (STA). We consider four kinds of coupling protocols and calculate the evolution of the mean phonon number of the mechanical resonator in both the adiabatic and STA cases. We verify that the ground-state cooling of the mechanical resonator can be achieved with the STA method in a much shorter period. The STA method can also be generalized to accelerate other adiabatic processes in cavity optomechanics, and hence this work will open up a new realm of fast optomechanical manipulations., 11 pages, 5 figures, 1 table

Non-Hermitian spectral degeneracies, known as exceptional points (EPs), feature simultaneous coalescence of both eigenvalues and the associated eigenstates of a system. A host of intriguing EP effects and their applications have been revealed in the classical realm, such as loss-induced lasing, single-mode laser, and EP-enhanced sensing. Here we show that a purely quantum effect, known as single-photon blockade, emerges in a Kerr microring resonator due to EP-induced asymmetric coupling between the optical modes and the nonlinearity-induced anharmonic energy-level spacing. A striking feature of this photon blockade is that it emerges at two-photon resonance which in Hermitian systems will only lead to photon-induced tunneling but not to photon blockade. By tuning the system towards to or away from an EP, one can control quantum correlations, implying the potential use of our system for frequency tunable single-photon generation and an antibunching-to-bunching light switch. Our work sheds new light on EP-engineered purely quantum effects, providing unique opportunities for making and utilizing various single-photon quantum EP devices., Comment: 8 pages, 4 figures

We propose a reliable scheme to recover the conventional photon blockade effect in the dispersive Jaynes-Cummings model, which describes a two-level atom coupled to a single-mode cavity field in the large-detuning regime. This is achieved by introducing a transversal driving to the atom and then photonic nonlinearity is obtained. The eigenenergy spectrum of the system is derived analytically and the photon blockade effect is confirmed by numerically calculating the photon-number distributions and equal-time second-order correlation function of the cavity field in the presence of system dissipations. We find that the conventional photon blockade effect can be recovered at proper atomic and cavity-field drivings. This work will provide a method to generate the conventional photon blockade effect in the dispersively coupled quantum optical systems., Comment: 9 pages, 6 figures

Multiphonon state plays an important role in quantum information processing and quantum metrology. Here we propose a scheme to realize dynamical emission of phonon pairs based on the technique of stimulated Raman adiabatic passage in a single cavity optomechanical system, where the optical cavity is driven by two Gaussian pulse lasers. By exploring quantum trajectories of the state populations and the average phonon number, we find that the dynamical phonon-pair emission can be realized under the appropriate parameter conditions and is tunable by controlling the time interval between the consecutive pulses of pump lasers. In particular, the numerical results for the standard and generalized second-order correlation functions of the mechanical mode show that the system can behave as an antibunched phonon-pair emitter. Our proposal can be extended to achieve an antibunched $n$-phonon emitter, which has potential applications for on-chip quantum communications., Comment: 8 pages, 5 figures

We study tunable optomechanically induced transparency by controlling the dark-mode effect induced by two mechanical modes coupled to a common cavity field. This is realized by introducing a phase-dependent phonon-exchange interaction, which is used to form a loop-coupled configuration. Combining this phase-dependent coupling with the optomechanical interactions, the dark-mode effect can be controlled by the quantum interference effect. In particular, the dark-mode effect in this two-mechanical-mode optomechanical system can lead to a double-amplified optomechanically induced transparency (OMIT) window and a higher efficiency of the second-order sideband in comparison with the standard optomechanical system. This is because the effective mechanical decay rate related to the linewidth of the OMIT window becomes a twofold increase in the weak-coupling limit. When the dark-mode effect is broken, controllable double transparency windows appear and the second-order sideband, as well as the light delay or advance, is significantly enhanced. For an N-mechanical-mode optomechanical system, we find that in the presence of the dark-mode effect, the amplification multiple of the linewidth of the OMIT window is nearly proportional to the number of mechanical modes, and that the OMIT with a single window becomes the one with N tunable windows by breaking the dark-mode effect. The study will be useful in optical information storage within a large-frequency bandwidth and multichannel optical communication based on optomechanical systems., 14 pages, 7 figures

Ultrastrong optomechanical interaction is a significant element for the study of the fundamentals and applications of optomechanical physics, but its realization remains a big challenge in the field of optomechanics. In this work, we propose a reliable scheme to realize a generalized ultrastrong optomechanical-like coupling in a cross-Kerr-type coupled two-bosonic-mode system, in which one of the two bosonic modes is strongly driven. The generalized optomechanical-like interaction takes the form of a product of the excitation number operator of one mode and the rotated quadrature operator of the other mode. Here, both the coupling strength and the phase angle of the rotated quadrature operator are tunable via the driving field. The optomechanical-like coupling can be strongly enhanced to enter the ultrastrong-coupling regime, where the few-photon optomechanical effects such as photon blockade and macroscopic quantum superposition become accessible. The controllability of the quadrature phase angle provides a new degree of freedom for the manipulation of optomechanical systems and enables the implementation of geometric quantum operations. We also present some discussions on the experimental implementation of this scheme. This study will pave the way to the study of quantum physics and quantum technology at the few-photon level in optomechanical systems.

We study the photon-blockade effect in a loop-coupled optomechanical system consisting of two cavity modes and one mechanical mode. Here, the mechanical mode is optomechanically coupled to the two cavity modes, which are coupled with each other via a photon-hopping interaction. By treating the photon-hopping interaction as a perturbation, we obtain the analytical results of the eigenvalues and eigenstates of the system in the subspaces associated with zero, one, and two photons. We find a phenomenon of optical normal-mode-induced phonon-sideband splitting in the photon-blockade effect by analytically and numerically calculating the second-order correlation functions of the two cavity modes. This work not only presents a method to choose optimal driving frequency for photon blockade by tuning the photon-hopping interaction, but also provides a means to characterize the normal-mode splitting with cavity photon statistics., Comment: 14 pages, 6 figures

The realization of multimode optomechanical interactions in the single-photon strong-coupling regime is a desired task in cavity optomechanics, but it remains a challenge in realistic physical systems. In this work, we propose a reliable scheme to simulate a three-mode optomechanical system working in the single-photon strong-coupling regime based on the Fredkin-type interaction. This is achieved by utilizing two strong drivings to the two exchangly-coupled modes in the Fredkin-type coupling involving one optical mode and two mechanical-like modes. As an application of this enhanced three-mode nonlinear optomechanical coupling, we show how to generate entangled-cat states of the mechanical-like modes using the conditional displacement mechanism. The quantum coherence effects in the generated states are investigated by calculating two-mode joint Wigner function and quantum entanglement. The influence of the dissipation effect on the state generation is considered in the open-system case., Comment: 11 pages, 8 figures

We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and atom-driving cases, and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blockade effect. Specifically, we show that quantum interference can enhance the photon blockade effect in the single-photon cavity-field-driving case. Our results are confirmed by analytically and numerically calculating the correlation function of the cavity-field mode. Our work has potential applications in quantum information processing and paves the way for the study of multiphoton quantum coherent devices., 15 pages, 9 figures

Quantum blockade and entanglement play important roles in quantum information and quantum communication as quantum blockade is an effective mechanism to generate single photons (phonons) and entanglement is a crucial resource for quantum information processing. In this work, we propose a method to generate single entangled photon-phonon pairs in a hybrid optomechanical system. We show that photon blockade, phonon blockade, and photon-phonon correlation and entanglement can be observed via the atom-photon-phonon (tripartite) interaction, under the resonant atomic driving. The correlated and entangled single photons and single phonons, i.e., single entangled photon-phonon pairs, can be generated in both the weak and strong tripartite interaction regimes. Our results may have important applications in the development of highly complex quantum networks., Comment: 9 pages, 7 figures

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators., Comment: 15 pages, 6 figures

Few-photon optomechanical effects are not only important physical evidences for understanding the radiation-pressure interaction between photons and mechanical oscillation, but also have wide potential applications in modern quantum technology. Here we study the few-photon optomechanical effects including photon blockade and generation of the Schr\"{o}dinger cat states under the assistance of a cross-Kerr interaction, which is an inherent interaction accompanied the optomechanical coupling in a generalized optomechanical system. By exactly diagonalizing the generalized optomechanical Hamiltonian and calculating its unitary evolution operator, we find the physical mechanism of the enhancement of photon blockade and single-photon mechanical displacement. The quantum properties in this generalized optomechanical system are studied by investigating the second-order correlation function of the cavity field and calculating the Wigner function and the probability distribution of the rotated quadrature operator for the mechanical mode. We also study the influence of the dissipations on the few-photon optomechanical effects., Comment: 16 pages, 11 figures

We study the spectrum of single-photon emission and scattering in a mixed optomechanical model which consists of both linear and quadratic optomechanical interactions. The spectra are calculated based on the exact long-time solutions of the single-photon emission and scattering processes in this system. We find that there exist some phonon sideband peaks in the spectra and there are some sub peaks around the phonon sideband peaks under proper parameter conditions. The correspondence between the spectral features and the optomechanical interactions is confirmed, and the optomechanical coupling strengths can be inferred by analyzing the resonance peaks and dips in the spectra., Comment: 9 pages, 6 figures

We propose how to create and manipulate one-way nonclassical light via photon blockade in rotating nonlinear devices. We refer to this effect as nonreciprocal photon blockade (PB). Specifically, we show that in a spinning Kerr resonator, PB happens when the resonator is driven in one direction but not the other. This occurs because of the {Fizeau drag,} leading to a full split of the resonance frequencies of the countercirculating modes. Different types of purely quantum correlations, such as single- and two-photon blockades, can emerge in different directions in a well-controlled manner, and the transition from PB to photon-induced tunneling is revealed as well. Our work opens up a new route to achieve quantum nonreciprocal devices, which are crucial elements in chiral quantum technologies or topological photonics., Comment: 8+28 pages, 4+9 figures, 2 tables

We propose a spectrometric method to detect a classical weak force acting upon the moving end mirror in a cavity optomechanical system. The force changes the equilibrium position of the end mirror, and thus the resonance frequency of the cavity field depends on the force to be detected. As a result, the magnitude of the force can be inferred by analyzing the single-photon emission and scattering spectra of the optomechanical cavity. Since the emission and scattering processes are much faster than the characteristic mechanical dissipation, the influence of the mechanical thermal noise is negligible in this spectrometric detection scheme. We also extent this spectrometric method to detect a monochromatic oscillating force by utilizing an optomechanical coupling modulated at the same frequency as the force., 16 pages, 6 figures

We propose a scheme to generate entangled coherent states (ECSs) of two microwave cavity fields coupling to a SQUID-based Cooper pair box (CPB) charge qubit by extending the single-cavity model of coupling between a single microcavity and a CPB charge qubit proposed by Liu et al (2005 Phys. Rev. A 71 063820). We show that by measuring the states of the CPB charge qubit, ECSs of the two cavity fields can be generated with a controllable interaction between the cavities and the CPB charge qubit.

In this paper, we propose an optical scheme to almost completely teleport a two-mode four-component entangled coherent state in terms of optical devices such as nonlinear Kerr media, beam splitters, phase shifters and photon detectors. Different from those previous schemes in which exact photon number discrimination is needed, in our scheme one only needs to make 'yes' and 'no' measurements upon the photon numbers in related modes. This scheme can also be understood as an entanglement swapping protocol.

We propose an approach to enhance the mechanical effects of single photons in a two-mode optomechanical system. This is achieved by introducing a resonance-frequency modulation to the cavity fields. When the modulation frequency and amplitude satisfy certain conditions, the mechanical displacement induced by single photons could be larger than the quantum zero-point fluctuation of the oscillating resonator. This method can be used to create distinct mechanical superposition states., 7 pages, 3 figures

In this paper, we study generation of entangled states in a system which consists of a single trapped ion in a cavity. We obtain a cross-Kerr-like interaction between the cavity field (photons) and the centre-of-mass motion (phonons) of the trapped ion in the Lamb–Dicke and large detuning regime. Based on this cross-Kerr-like interaction, we create hybrid entangled states between the phonon mode and the ionic internal states, and between the cavity field and ionic internal states, respectively. We also show that it is possible to prepare entangled coherent states between the cavity field and the phonon mode. We explicitly obtain an entangled state between two pairs of Schrodinger-cat states.

We propose a new optical scheme for the quantum teleportation of superposed coherent states (SCSs) in terms of optical elements. Our scheme can realize a near-complete quantum teleportation of SCSs with arbitrary coefficients. Different from previous schemes, our protocol need only yes or no measurements of the photon numbers of the related modes instead of the exact measurements of the photon numbers in the previous schemes.

We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon., Comment: 10 pages, 7 figures

We propose a spectrometric method to reconstruct the motional states of mechanical modes in optomechanics. This is achieved by detecting the single-photon emission and scattering spectra of the optomechanical cavity. Owing to an optomechanical coupling, the \emph{a priori} phonon-state distributions contribute to the spectral magnitude, and hence we can infer information on the phonon states from the measured spectral data. When the single-photon optomechanical-coupling strength is moderately larger than the mechanical frequency, then our method works well for a wide range of cavity-field decay rates, irrespective of whether or not the system is in the resolved-sideband regime., Comment: 9 pages, 4 figures

We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should work in the single-photon strong-coupling regime and the deep-resolved-sideband regime., Comment: 5 pages, 3 figures, Phys. Rev. A in press

Quantum squeezing in mechanical systems is not only a key signature of macroscopic quantum effects, but can also be utilized to advance the metrology of weak forces. Here we show that strong mechanical squeezing in the steady state can be generated in an optomechanical system with mechanical nonlinearity and red-detuned monochromatic driving on the cavity mode. The squeezing is achieved as the joint effect of nonlinearity-induced parametric amplification and cavity cooling, and is robust against thermal fluctuations of the mechanical mode., Comment: 8 pages, 5 figures, published in PRA

Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the quantum coherence of an optomechanical system with a dressed-state master equation approach. Our master equation includes photon-number-dependent terms that induce dephasing in this system. Cavity dephasing, second-order photon correlation, and two-cavity entanglement are studied with the dressed-state master equation., Comment: 8 pages, 4 figures, published

We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-sideband and single-photon strong-coupling regimes, the single-photon resonant driving will induce a photon blockade, which is limited by the thermal noise of the mechanical environment., 6 pages, 4 figures

It is well-known that the nonlinear coupling between a mechanical oscillator and a superconducting oscillator or optical cavity can be used to generate a Kerr-nonlinearity for the cavity mode. We show that the strength of this Kerr-nonlinearity, as well as the effect of the photon-pressure force can be enormously increased by modulating the strength of the nonlinear coupling. We present an electromechanical circuit in which this enhancement can be readily realized., 5 pages, revtex4-1, 1 png figure

We present an analytic solution describing the quantum state of a single photon after interacting with a moving mirror in a cavity. This includes situations when the photon is initially stored in a cavity mode as well as when the photon is injected into the cavity. In addition, we obtain the spectrum of the output photon in the resolved-sideband limit, which reveals spectral features of the single-photon strong-coupling regime in this system. We also clarify the conditions under which the phonon sidebands are visible and the photon-state frequency shift can be resolved., 5 pages, 5 figures

We study the photon blockade of two-photon scattering in a one-dimensional waveguide, which contains two atoms coupled via the Rydberg interaction. We obtain the analytic scattering solution of photonic wave packets with the Laplace transform method. We examine the photon correlation by addressing the two-photon relative wave function and the second-order correlation function in the single- and two-photon resonance cases. It is found that, under the single-photon resonance condition, photon bunching and antibunching can be observed in the two-photon transmission and reflection, respectively. In particular, the bunching and antibunching effects become stronger with the increasing of the Rydberg coupling strength. In addition, we find a phenomenon of bunching-antibunching transition caused by the two-photon resonance., Comment: 9 pages, 4 figures

We present an exact analytical solution of the two-photon scattering in a cavity optomechanical system. This is achieved by solving the quantum dynamics of the total system, including the optomechanical cavity and the cavity-field environment, with the Laplace transform method. The long-time solution reveals detailed physical processes involved as well as the corresponding resonant photon frequencies. We characterize the photon correlation induced in the scattering process by calculating the two-photon joint spectrum of the long-time state. Clear evidence for photon frequency anti-correlation can be observed in the joint spectrum. In addition, we calculate the equal-time second-order correlation function of the cavity photons. The results show that the radiation pressure coupling can induce photon blockade effect, which is strongly modulated by the phonon sideband resonance. In particular, we obtain an explicit expression of optomechanical coupling strength determining these sideband modulation peaks based on the two-photon resonance condition., Comment: 10 pages, 6 figures

We propose a method to generate quadrature squeezed states of a moving mirror in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the cavity is driven by an external field with a large detuning, the moving mirror behaves as a parametric oscillator. We show that parametric resonance can be reached approximately by modulating the driving field amplitude at a frequency matching the frequency shift of the mirror. The parametric resonance leads to an efficient generation of squeezing, which is limited by the thermal noise of the environment., Comment: 4 pages, 2 figures

We investigate the response of a harmonically confined mirror to an optical pulse in cavity optomechanics. We show that when the pulsed coupling strength takes the form of a chirped pulse, thermal fluctuations of the mirror can be significantly transferred to the cavity field. In addition, the frequency modulation of the pulse could enable a better cooling performance by suppressing the sensitivity of the dependence of detuning and pulse areas. Using numerical investigations, we find that the pulsed-cooling is mainly limited by the cavity-field decay rate., Comment: 6 pages, 4 figures

We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present analytic solution of quantum states of the transmitted and reflected two photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerge after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in the relative coordinates, which is a feature that may be interpreted as a two-photon bound state in this waveguide-cavity system., Comment: 9 pages, 5 figures

We theoretically study how to control transport, bound states, and resonant states of a single photon in a one-dimensional coupled-cavity array. We find that the transport of a single photon in the cavity array can be controlled by tuning the frequency of either one or two cavities. If one of the cavities in the array has a tunable frequency, and its frequency is tuned to be larger (or smaller) than those of other cavities, then there is a photon bound state above (or below) the energy band of the coupled cavity array. However, if two cavities in the array have tunable frequencies, then there exist both bound states and resonant states. When the frequencies of the two cavities are chosen to be much larger than those of other cavities and the hopping couplings between any two nearest-neighbor cavities are weak, a single photon with a resonant wave vector can be trapped in the region between the two frequency-tunable cavities. In this case, a quantum supercavity can be formed by these two frequency-tunable cavities. We also study how to apply this photon transport control to an array of coupled superconducting transmission line resonators., 10 pages, 11 figures, references updated