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Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object—in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the “bomb test” with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett–Garg inequality—a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett–Garg inequality.

We investigate the ground-state properties of the Anderson single impurity model (finite Coulomb impurity repulsion) with the Coupled Cluster Method. We consider different CCM reference states and approximation schemes and make comparison with exact Green's function results for the non-interacting model and with Brillouin–Wigner perturbation theory for the full interacting model. Our results show that coupled cluster techniques are well suited to quantum impurity problems.

We describe a technique to emulate the dynamics of two-level P T -symmetric spin Hamiltonians, replete with gain and loss, using the unitary dynamics of a larger quantum system. The two-level system in question is embedded in a subspace of a four-level Hamiltonian, with the exterior levels acting as reservoirs. The emulation time is normally finite, limited by the depletion of the reservoirs. We show that it is possible to emulate the desired behaviour of the P T -symmetric Hamiltonian without depleting the reservoir levels, by including an additional coupling between them. This extends the emulation time indefinitely, when in the unbroken symmetry phase of the non-unitary P T dynamics. We propose a realistic experimental implementation using dynamically decoupled magnetic sublevels of ultracold atoms.

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels $N$ that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small $N$, that exceed the known bound for the Leggett-Garg inequality, and show that in the limit $N\rightarrow \infty$ the Leggett-Garg inequality can be violated up to its algebraic maximum., 6 pages, 2 figures

We consider a driven single mode Dicke-Hamiltonian coupled to a dissipative zero-temperature bath. We derive the cumulant generating function for emitted photons of this quantum-critical system by using a $P$-representation of the master equation in the thermodynamic limit. This cumulant generating function is shown to consist of two parts: a macroscopic component, which is Poissonian in nature with characteristic rate proportional to the order parameter of the system; and a part describing fluctuations which is non-trivial in form and divergent around the quantum phase transition., Comment: 9 pages, 5 figures

We present a transport setup of coupled quantum dots that enables the creation of spatially separated spin-entangled two-electron dark states. We prove the existence of an entangled transport dark state by investigating the system Hamiltonian without coupling to the electronic reservoirs. In the transport regime the entangled dark state which corresponds to a singlet has a strongly enhanced Fano factor compared to the dark state which corresponds to a mixture of the triplet states. Furthermore we calculate the concurrence of the occupying electrons to show the degree of entanglement in the transport regime., Comment: 9 pages and 3 figures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence., We present a theoretical study of a hybrid circuit-quantum electrodynamics system composed of two semiconducting charge-qubits confined in a microwave resonator. The qubits are defined in terms of the charge states of two spatially separated double quantum dots (DQDs) which are coupled to the same photon mode in the microwave resonator. We analyse a transport setup where each DQD is attached to electronic reservoirs and biased out-of-equilibrium by a large voltage, and study how electron transport across each DQD is modified by the coupling to the common resonator. In particular, we show that the inelastic current through each DQD reflects an indirect qubit-qubit interaction mediated by off-resonant photons in the microwave resonator. As a result of this interaction, both charge qubits stay entangled in the steady (dissipative) state. Finite shot noise cross-correlations between currents across distant DQDs are another manifestation of this nontrivial steady-state entanglement. © IOP Publishing and Deutsche Physikalische Gesellschaft., This work was supported by the European Commission (STREP PICC), the Alexander von Humboldt Foundation, the DAAD and DFG grant numbers BR 1528/7-1, 1528/8-1, SFB 910 and GRK 1558 and the Spanish MINECO through grant numbers FIS2009-08744 and FIS2012-33521.

We establish a set of nonequilibrium quantum phase transitions in the Ising model driven under monochromatic nonadiabatic modulation of the transverse field. We show that besides the Ising-like critical behavior, the system exhibits an anisotropic transition which is absent in equilibrium. The nonequilibrium quantum phases correspond to states which are synchronized with the external control in the long-time dynamics., Comment: 10 pages, 5 figures. Published in Physical Review A

We consider an ensemble of three-level particles in lambda-configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke-model. We show that in the thermodynamic limit this model supports a superradiant quantum phase transition. Remarkably, this can be both a first and a second order phase transition. A connection of the phase diagram to the symmetries of the Hamiltonian is also given. In addition, we show that this model can describe atoms interacting with an electromagnetic field in which the microscopic Hamiltonian includes a diamagnetic contribution. Even though the parameters of the atomic system respect the Thomas--Reiche--Kuhn sum rule, the system still shows a superradiant phase transition., Comment: 9 pages, 3 figures

We consider maximal violations of the Leggett-Garg inequality, obtained by maximising over all possible measurement operators, in relation to non-unitary aspects of the system dynamics. We model the action of an environment on a qubit in terms of generic quantum channels and relate the maximal value of the Leggett-Garg correlator to the channel parameters. We focus on unital channels, and hence on decoherence. In certain important cases, exact relations between the channel parameters and maximal violations can be found. Moreover, we demonstrate the existence of distinct thresholds for the channel parameters, below which no violation of the Leggett-Garg inequality can occur., 7 pages; 3 figures

We establish a set of nonequilibrium quantum phase transitions in the Lipkin-Meshkov-Glick model under monochromatic modulation of the inter-particle interaction. We show that the external driving induces a rich phase diagram that characterizes the multistability in the system. Interestingly, the number of stable configurations can be tuned by increasing the amplitude of the driving field. Furthermore, by studying the quantum evolution, we demonstrate that the system exhibits a set of quantum phases that correspond to dynamically stabilized states., 9 pages, 4 figures. This version contains corrected typos, new references, new figures, and a new appendix. Comments are welcome

We consider the violation of the Leggett-Garg inequality in electronic Mach-Zehnder inteferometers. This set-up has two distinct advantages over earlier quantum-transport proposals: firstly, the required correlation functions can be obtained without time-resolved measurements. Secondly, the geometry of an interferometer allows one to construct the correlation functions from ideal negative measurements, which addresses the non-invasiveness requirement of the Leggett-Garg inequality. We discuss two concrete realisations of these ideas: the first in quantum Hall edge-channels, the second in a double quantum dot interferometer., 11 pages, 5 figures

Made available in DSpace on 2022-04-29T04:22:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-07-18 We consider the Dicke model in the ultrastrong-coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers N for bosonic and fermionic systems. We derive partition functions with degeneracy factors that account for the number of configurations and derive explicit expressions for the Landau free energy. This allows us to discuss the difference between the original Dicke (fermionic) and the bosonic case. We find a crossover between these two cases that shows up, for example, in the specific heat. © 2012 American Physical Society. Instituto de Física Teórica UNESP-São Paulo State University, Caixa Postal 70532-2, 01156-970 São Paulo, SP Institut für Theoretische Physik TU Berlin, Hardenbergstr. 36, D-10623 Berlin Instituto de Física Teórica UNESP-São Paulo State University, Caixa Postal 70532-2, 01156-970 São Paulo, SP

We derive a set of Leggett-Garg inequalities (temporal Bell's inequalities) for the moment generating function of charge transferred through a conductor. Violation of these inequalities demonstrates the absence of a macroscopic-real description of the transport process. We show how these inequalities can be violated by quantum-mechanical systems and consider transport through normal and superconducting single-electron transistors as examples., Comment: 5 pages; 3 figures

We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix of the system resolved with respect to the number of transported charges enables the evaluation of the noise and higher-order cumulants of the full counting statistics. We apply this formalism to an analytically solvable model of a single-level quantum dot coupled to highly biased leads with Lorentzian energy-dependent tunnel coupling and demonstrate that, although reproducing exactly the mean current, the resonant tunneling approximation is not exact for the noise and higher order cumulants. Even if it may fail in the regime of strongly non-Markovian dynamics, this approach generically improves results of lower-order and/or Markovian approaches., Comment: 5 pages, 1 figure; little changes; very similar to the published version

We theoretically study an extension of the Dicke model, where the single-particle Hamiltonian has three energy levels in Lambda-configuration, i.e. the excited state is coupled to two non-degenerate ground states via two independent quantized light fields. The corresponding many-body Hamiltonian can be diagonalized in the thermodynamic limit with the help of a generalized Holstein--Primakoff transformation. Analyzing the ground-state energy and the excitation energies, we identify one normal and two superradiant phases, separated by phase transitions of both first and second order. A phase with both superradiant states coexisting is not stable. In addition, in the limit of two degenerate ground states a dark state emerges, which seems to be analogous to the dark state appearing in the well known stimulated Raman adiabatic passage scheme., 9 pages, 6 figures

We discuss the description of full counting statistics in quantum transport with a nonMarkovian master equation. We focus on differences arising from whether charge is considered as a classical or a quantum degree of freedom. These differences manifest themselves in the inhomogeneous term of the master equation which describes initial correlations. We describe the influence on current and in particular, the finite-frequency shotnoise. We illustrate these ideas by studying transport through a quantum dot and give results that include both sequential and cotunneling processes. Importantly, the noise spectra derived from the classical description are essentially frequency-independent and all quantum noise effects are absent. These effects are fully recovered when charge is considered as a quantum degree of freedom., Comment: 12 pages; 3 figures

We establish a set of nonequilibrium quantum phase transitions in the Dicke model by considering a monochromatic nonadiabatic modulation of the atom-field coupling. For weak driving the system exhibits a set of sidebands which allow the circumvention of the no-go theorem which otherwise forbids the occurence of superradiant phase transitions. At strong driving we show that the system exhibits a rich multistable structure and exhibits both first- and second-order nonequilibrium quantum phase transitions., 4 pages, 3 Figures, and supplementary material. This new version contains corrected typos, new references and new versions of the figures. Published by Physical Review Letters

We propose a feedback control scheme for generating and stabilizing pure states of transport devices, such as charge qubits, under non-equilibrium conditions. The purification of the device state is conditioned on single electron jumps and leaves a clear signal in the full counting statistics which can be used to optimize control parameters. As an example of our control scheme, we are presenting the stabilization pure transport states in a double quantum dot setup with the inclusion of phonon dephasing., 7 pages, 5 figures

We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As specific detector model we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust initialization of solid-state qubits in quantum computational algorithms at arbitrary temperatures., 4 pages, 4 figures, supplementary material, with minor modifications to be published by PRL

We present a theory of finite-frequency noise in non-equilibrium conductors. It is shown that Non-Markovian correlations are essential to describe the physics of quantum noise. In particular, we show the importance of a correct treatment of the initial system-bath correlations, and how these can be calculated using the formalism of quantum master equations. Our method is particularly important in interacting systems, and when the measured frequencies are larger that the temperature and applied voltage. In this regime, quantum-noise steps are expected in the power spectrum due to vacuum fluctuations. This is illustrated in the current noise spectrum of single resonant level model and of a double quantum dot --charge qubit-- attached to electronic reservoirs. Furthermore, the method allows for the calculation of the single-time counting statistics in quantum dots, measured in recent experiments., Comment: 9 Pages, 7 Figures. Published version

We describe a method for calculating the counting statistics of electronic transport through nanoscale devices with both sequential and cotunneling contributions. The method is based upon a perturbative expansion of the von Neumann equation in Liouvillian space, with current cumulants calculated from the resulting nonMarkovian master equation without further approximation. As application, we consider transport through a single quantum dot and discuss the effects of cotunneling on noise and skewness, as well as the properties of various approximation schemes., Comment: 11 pages, 6 figures

We study the transport properties of the Fano-Anderson model with a Lorentzian-shaped density of states in one of the electronic reservoirs. We explicitly show that the energy dependence of the density of states can cause non-Markovian effects and that the non-Markovian master equation may fail if these effects are strong. We evaluate the stationary current, the zero frequency current noise and the occupation dynamics of the resonant level by means of a quantum master equation approach within different approximation schemes and compare the results to the exact solution obtained by scattering theory and Green's functions., 9 pages, 6 figures; due to suggestions of a referee we have added an appendix where our kernel is derived in detail; a few typos are corrected

We consider theoretically the transport through the double quantum dot structure of the recent experiment of C. Payette {\it et al.} [Phys. Rev. Lett. {\bf 102}, 026808 (2009)] and calculate stationary current and shotnoise. Three-level mixing gives rise to a pronounced current suppression effect, the character of which charges markedly with bias direction. We discuss these results in connexion with the dark states of coherent population trapping in quantum dots., Comment: 6 pages, 5 figs

We study the relationship between entanglement and parametric resonance in a system of two coupled time-dependent oscillators. As a measure of bipartite entanglement, we calculate the linear entropy for the reduced density operator, from which we study the entanglement dynamics. In particular, we find that the bipartite entanglement increases in time up to a maximal mixing scenario, when the set of auxiliary dynamical parameters are under parametric resonance. Moreover, we obtain a closed relationship between the correlations in the ground state, the localisation of the Wigner function in phase space, and the localisation of the wave function of the total system., Comment: 10 pages, 5 figures

We present a formalism to calculate finite-frequency current correlations in interacting nanoscale conductors. We work within the n-resolved density matrix approach and obtain a multi-time cumulant generating function that provides the fluctuation statistics, solely from the spectral decomposition of the Liouvillian. We apply the method to the frequency-dependent third cumulant of the current through a single resonant level and through a double quantum dot. Our results, which show that deviations from Poissonian behaviour strongly depend on frequency, demonstrate the importance of finite-frequency higher-order cumulants in fully characterizing interactions., Comment: 4 pages, 2 figures, improved figures & discussion. J-ref added

We apply the time-delayed Pyragas control scheme to the dissipative Dicke model via a modulation of the atom-field-coupling. The feedback creates an infinite sequence of non-equilibrium phases with fixed points and limit cycles in the primary superradiant regime. We analyse this Hopf bifurcation scenario as a function of delay time and feedback strength, and determine analytical conditions for the phase boundaries.

We propose an experiment to observe coherent oscillations in a single quantum dot with the oscillations driven by spin-orbit interaction. This is achieved without spin-polarised leads, and relies on changing the strength of the spin-orbit coupling via an applied gate pulse. We derive an effective model of this system which is formally equivalent to the Jaynes-Cummings model of quantum optics. For parameters relevant to a InGaAs dot, we calculate a Rabi frequency of 2 GHz., Comment: 4 pages, 3 figures Revised version: additional results included on page 4. Fig 3c replaced accordingly. Numerical error in predicted Rabi frequency corrected

We describe a mechanism for the production of polarization-entangled microwaves using intraband transitions in a pair of quantum dots. This proposal relies neither on spin-orbit coupling nor on control over electron-electron interactions. The quantum correlation of microwave polarizations is obtained from orbital degrees of freedom in an external magnetic field. We calculate the concurrence of emitted microwave photon pairs and show that a maximally entangled Bell pair is obtained in the limit of weak interdot coupling.

Building on a previous proposal for the entanglement of electron-hole pairs in the Fermi sea, we show how 3 qubits can be entangled without using electron-electron interactions. As in the 2-qubit case, this electronic scheme works even if the sources are in (local) thermal equilibrium -- in contrast to the photonic analogue. The 3 qubits are represented by 4 edge-channel excitations in the quantum Hall effect (2 hole excitations plus 2 electron excitations with identical channel index). The entangler consists of an adiabatic point contact flanked by a pair of tunneling point contacts. The irreducible 3-qubit entanglement is characterized by the tangle, which is expressed in terms of the transmission matrices of the tunneling point contacts. The maximally entangled Greenberger-Horne-Zeilinger (GHZ) state is obtained for channel-independent tunnel probabilities. We show how low-frequency noise measurements can be used to determine an upper and lower bound to the tangle. The bounds become tighter the closer the electron-hole state is to the GHZ state., 8 pages including 4 figures; [2017: fixed broken postscript figures]

It is known that a quantum computer operating on electron-spin qubits with single-electron Hamiltonians and assisted by single-spin measurements can be simulated efficiently on a classical computer. We show that the exponential speed-up of quantum algorithms is restored if single-charge measurements are added. These enable the construction of a CNOT (controlled NOT) gate for free fermions, using only beam splitters and spin rotations. The gate is nearly deterministic if the charge detector counts the number of electrons in a mode, and fully deterministic if it only measures the parity of that number., Comment: 5 pages including 3 figures

We consider a class of generalised single mode Dicke Hamiltonians with arbitrary boson coupling in the pseudo-spin $x$-$z$ plane. We find exact solutions in the thermodynamic, large-spin limit as a function of the coupling angle, which allows us to continuously move between the simple dephasing and the original Dicke Hamiltonians. Only in the latter case (orthogonal static and fluctuating couplings), does the parity-symmetry induced quantum phase transition occur., Comment: 6 pages, 5 figues

For two qubits in a pure state there exists a one-to-one relation between the entanglement measure (the concurrence ${\cal C}$) and the maximal violation ${\cal M}$ of a Bell inequality. No such relation exists for the three-qubit analogue of ${\cal C}$ (the tangle $\tau$), but we have found that numerical data is consistent with a simple set of upper and lower bounds for $\tau$ given ${\cal M}$. The bounds on $\tau$ become tighter with increasing ${\cal M}$, so they are of practical use. The Svetlichny form of the Bell inequality gives tighter bounds than the Mermin form. We show that the bounds can be tightened further if the tangle is replaced by an entanglement monotone that can identify both the W state and the Greenberger-Horne-Zeilinger state., Comment: 3 pages, 2 figures

We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of $N$ two-level atoms. This model exhibits a zero-temperature quantum phase transition in the $N \go \infty$ limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite $N$ and, by analysing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase-transition. Our considerations of the wavefunction indicate that this is connected with a delocalisation of the system and the emergence of macroscopic coherence. We also derive a semi-classical Dicke model, which exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos., 51 pages, 15 figures, latex

We demonstrate theoretically that the shot noise produced by a tunnel barrier in a two-channel conductor violates a Bell inequality. The nonlocality is shown to originate from entangled electron-hole pairs created by tunneling events---without requiring electron-electron interactions. The degree of entanglement (concurrence) equals $2({T}_{1}{T}_{2}{)}^{1/2}({T}_{1}+{T}_{2}{)}^{\ensuremath{-}1}$, with ${T}_{1},{T}_{2}\ensuremath{\ll}1$ the transmission eigenvalues. A pair of edge channels in the quantum Hall effect is proposed as an experimental realization.

The two-photon Rabi Hamiltonian is a simple model describing the interaction of light with matter, with the interaction being mediated by the exchange of two photons. Although this model is exactly soluble in the rotating-wave approximation, we work with the full Hamiltonian, maintaining the non-integrability of the model. We demonstrate that, despite this non-integrability, there exist isolated, exact solutions for this model analogous to the so-called Juddian solutions found for the single-photon Rabi Hamiltonian. In so doing we use a Bogoliubov transformation of the field mode, as described by the present authors in an earlier publication., 15 Pages, 1 Figure, Latex, minor changes

We present a scheme for creating and measuring entanglement between two double quantum dot charge qubits in a transport set-up in which voltage pulses can modify system parameters. Detection of entanglement is performed via the construction of a Bell inequality with current correlation measurements. An essential feature is the use of the internal dynamics of the qubits as the constituent electrons tunnel into the leads to give the single-particle rotations necessary for the Bell measurement., Comment: 5 pages, 3 figures

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localisation-delocalisation transition in which a macroscopic superposition is generated. We also describe the classical analogues of this behaviour., 4 pages, 5 figures, minor changes, Journal ref. added

We present a formalism for studying the behaviour of quantum systems coupled to nonequilibrium environments exhibiting nonGaussian fluctuations. We discuss the role of a qubit as a detector of the statistics of environmental fluctuations, as well as nonMarkovian effects in both weak and strong coupling limits. We also discuss the differences between the influences of classical and quantum environments. As examples of the application of this formalism we study the dephasing and relaxation of a charge qubit coupled to nonequillibrium electron transport through single and double quantum dots., 12 pages, 7 figures; significantly expanded version

The Rabi Hamiltonian is a simple, yet non-trivial model of light-matter interactions. Here we present a brief review of the application of the normal coupled cluster method (NCCM) to this model. We concentrate on the NCCM description of the excitation spectrum and of simple time evolutions of the system, providing a link between the two that limits the accuracy of NCCM dynamical calculations in practice.