I show that entanglement between two qubits can be generated if the two qubits interact with a common heat bath in thermal equilibrium, but do not interact directly with each other. In most situations the entanglement is created for a very short time after the interaction with the heat bath is switched on, but depending on system, coupling, and heat bath, the entanglement may persist for arbitrarily long times. This mechanism sheds new light on the creation of entanglement. A particular example of two quantum dots in a closed cavity is discussed, where the heat bath is given by the blackbody radiation.
We propose a scheme to for fast conditional phase shift and creation entanglement of two qubits that interact with a common heat bath. Dynamical decoupling is applied in the scheme so that it works even in the regime of strong interaction between qubits and environment. Our scheme does not request any direct interaction between the two qubits.
In a recent paper, PRL 114 100404, 2015, Raeisi and Mosca gave a limit for cooling with Heat-Bath Algorithmic Cooling (HBAC). Here we show how to exceed that limit by having correlation in the qubits-bath interaction.
The free energy of a quantum oscillator in an arbitrary heat bath at a temperature T is given by a "remarkable formula" which involves only a single integral. This leads to a corresponding simple result for the entropy. The low temperature limit is examined in detail and we obtain explicit results both for the case of an Ohmic heat bath and a radiation heat bath. More general heat bath models are also examined. This enables us to determine the entropy at zero temperature in order to check the third law of thermodynamics in the quantum regime
We reveal the potentially important role of a general mechanism that has hitherto not been invoked in quantum heat management schemes, namely, spectral filtering of the coupling between the heat baths in the setup and the quantum system that controls the heat flow. Such filtering is enabled by interfaces between the system and the baths by means of harmonic-oscillator modes whose resonant frequencies and coupling strengths are used as control parameters of the system-bath coupling spectra. We show that this uniquely quantum-electrodynamic mechanism, here dubbed bath spectral filtering, boosts …
We demonstrate in a very general fashion, considerable slowing down of decoherence and relaxation by fast frequency modulation of the system heat bath coupling. The slowing occurs as the decoherence rates are now determined by the spectral components of bath correlations which are shifted due to fast modulation. We present several examples including the slowing down of the heating of a trapped ion, where the system - bath interaction is not necessarily Markovian.
We investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity with respect to the cold bath. As a working medium, we use a two-level system and a harmonic oscillator that interact with a moving heat bath and a static cold bath. In the current work, the quantum heat engine is studied in the high and low temperatures regime. Using quantum thermodynamics and the theory of open quantum system we obtain the total produced work, the efficiency and the efficiency at maxim…
We report here the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance (NMR) of a solid-state ensemble three-qubit system.
Quantum heat transfer is analyzed in nonequilibrium two-qubits systems by applying the nonequilibrium polaron-transformed Redfield equation combined with full counting statistics. Steady state heat currents with weak and strong qubit-bath couplings are clearly unified. Within the two-terminal setup, the negative differential thermal conductance is unraveled with strong qubit-bath coupling and finite qubit splitting energy. The partially strong spin-boson interaction is sufficient to show the negative differential thermal conductance. Based on the three-terminal setup, that two-qubits are asymm…
The performance characteristics of a heat rectifier and a heat pump are studied in a non Markovian framework. The device is constructed from a molecule connected to a hot and cold reservoir. The heat baths are modelled using the stochastic surrogate Hamiltonian method. The molecule is modelled by an asymmetric double-well potential. Each well is semi-locally connected to a heat bath composed of spins. The dynamics is driven by a combined system-bath Hamiltonian. The temperature of the baths is regulated by a secondary spin bath composed of identical spins in thermal equilibrium. A random swap …
Probing Non-equilibrium baths: Frequency-Resolved Thermometry and Quantum Heat Current Turnover
Institute for Theoretical Physics, Department of Quantum and Classical Dynamics, Johannes Kepler Universität Linz（林茨约翰·开普勒大学理论物理系量子与经典动力学部）；Schulich Faculty of Chemistry and Helen Diller Quantum Center, Technion-Israel Institute of Technology（以色列理工学院舒利希化学学院及海伦·迪勒量子中心）
We suggest alternative quantum Otto engines, using heat bath algorithmic cooling with partner pairing algorithm instead of isochoric cooling. Liquid state nuclear magnetic resonance systems in one entropy sink are considered as working fluids. Then, the extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke type of quantum Otto engines. The role of heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two. Also, this cooling algorithm increases the power of engines reducing the time required for one cycle.
In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration o…
We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos on the one hand, and ballistic or diffusive energy absorption on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high resolution Wigner functions at long times, where the…
For heat engines working between two heat baths, functionality is often conditioned on a set of fixed constraints such as given internal structure of the engine and given temperatures for the baths. It is, however, important to devise heat engines which can function adaptively, in particular when the engine is a quantum system and the baths are subject to fluctuations. Here we study a model for an adaptive quantum heat engine whose heat baths can have variable temperatures. We obtain conditions under which such an engine can still operate. Moreover, we propose an enhancement of the heat engine…
The time evolution of occupation number is studied for fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of characteristics of thermal reservoirs of different statistics on the non-stationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.
Considering a kicked rotor coupled to a model heat bath both the classical and quantum entropy productions are calculated exactly. Starting with an initial wave packet, the von Neuman entropy as a function of time is determined from the reduced density matrix while the Liouville evolution of the corresponding Husimi distribution provides us with the classical entropy. It is found that both these entropies agree reasonably satisfying the same asymptotic growth law and more importantly both are proportional to the classical Liapounov exponent.
Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand,…
Quantum technologies require pure states, which are often generated by extreme refrigeration. Heat-bath algorithmic cooling is the theoretically optimal refrigeration technique: it shuttles entropy from a multiparticle system to a thermal bath, thereby generating a quantum state with a high degree of purity. Here, we show how to surpass this hitherto-optimal technique by taking advantage of a single binary-outcome measurement. Our protocols can create arbitrary numbers of pure quantum states without any residual mixedness by using a recently discovered device known as a quantum switch to put t…
We solve analytically master equations that describe a cavity filled with a kerr medium, taking into account the dissipation induced by the environment, and parametric down conversion processes. We use superoperator techniques.
Thermal Markovian dynamics is typically obtained by coupling a system to a sufficiently hot bath with a large heat capacity. Here we present a scheme for inducing Markovian dynamics using an arbitrarily small and cold heat bath. The scheme is based on injecting phase noise to the small bath. Several unique signatures of small bath are studied. We discuss realizations in ion traps and superconducting qubits and show that it is possible to create an ideal setting where the system dynamics is indifferent to the internal bath dynamics.
The quantum thermalization of the Jaynes-Cummings (JC) model in both equilibrium and non-equilibrium open-system cases is sdudied, in which the two subsystems, a two-level system and a single-mode bosonic field, are in contact with either two individual heat baths or a common heat bath. It is found that in the individual heat-bath case, the JC model can only be thermalized when either the two heat baths have the same temperature or the coupling of the JC system to one of the two baths is turned off. In the common heat-bath case, the JC system can be thermalized irrespective of the bath tempera…
We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. We calculate \emph{exactly} the time development of this non-Gaussian state due to interaction with an \emph{arbitrary} heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.
The finite coupled bosonic model of reservoir introduced by Vasile et al. [1] to characterize non-Markovianity, is used to study the different dissipative behaviors of a harmonic oscillator coupled to it when it is in resonance, close to resonance or far detuned. We show that information and energy exchange between system and heat bath go hand in hand because phonons are the carriers of both: in resonance free propagation of excitations is achieved, and therefore pure dissipation, while when far detuned the system can only correlate with the first oscillator in the bath's chain, leading to alm…
Entanglement sudden death in spatially separated two-mode Gaussian states coupled to local thermal and squeezed thermal baths is studied by mapping the problem to that of the quantum-to-classical transition. Using Simon's criterion concerning the characterisation of classicality in Gaussian states, the time to ESD is calculated by analysing the covariance matrices of the system. The results for the two-mode system at T=0 and T>0 for the two types of bath states are generalised to $n$-modes, and are shown to be similar in nature to the results for the general discrete $n$-qubit system.
Here the problem considered is that of a pair of oscillators coupled to a common heat bath. Many, if not most, discussions of a single operator coupled to a bath have used the independent oscillator model of the bath. However, that model has no notion of separation, so the question of phenomena when the oscillators are near one another compared with when they are widely separated cannot be addressed. Here the Lamb model of an oscillator attached to a stretched string is generalized to illustrate some of these questions. The coupled Langevin equations for a pair of oscillators attached to the s…
We propose a generation of a low-noise state of optomechanical oscillator by a temperature dependent force. We analyze the situation in which a quantum optomechanical oscillator (denoted as the membrane) is driven by an external force (produced by the piston). Both systems are embedded in a common heat bath at certain temperature $T$. The driving force the piston exerts on the membrane is bath temperature dependent. Initially, for $T=T_0$, the piston is linearly coupled to the membrane. The bath temperature is then reversibly changed to $T\neq T_0$. The change of temperature shifts the membran…
It is common knowledge that coupling to a heat bath, in general, tends to reduce the entanglement in a quantum system. In recent years, increasing interest has been devoted to the opposite situation where thermal or specifically tailored environments may stabilize or even generate entanglement. We prove the universality of this phenomenon for multipartite entanglement in the frame of an exactly solvable dephasing model. We show by evaluating analytical lower bounds for the appropriate entanglement measures that a common thermal environment can dynamically generate all entanglement classes of t…
A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability of that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. We also argue that the probability of the violation of the second law of thermodynamics (here in the form of net heat tran…
Controlled preparation of highly pure quantum states is at the core of practical applications of quantum information science, from the state initialization of most quantum algorithms to a reliable supply of ancilla qubits that satisfy the fault-tolerance threshold for quantum error correction. Heat-bath algorithmic cooling has been shown to purify qubits by controlled redistribution of entropy and multiple contact with a bath, not only for ensemble implementations but also for technologies with strong but imperfect measurements. However, an implicit restriction about the interaction with the b…
The effect of a thermal reservoir is investigated on a bipartite Gaussian state. We derive a pre-Lindblad master equation in the non-rotating wave approximation for the system. We then solve the master equation for a bipartite harmonic oscillator Hamiltonian with entangled initial state. We show that for strong damping the loss of entanglement is the same as for freely evolving particles. However, if the damping is small, the entanglement is shown to oscillate and eventually tend to a constant nonzero value.
We propose a new form of the Second Law inequality that defines a tight bound for extractable work from the non-equilibrium quantum state. In classical thermodynamics, the optimal work is given by the difference of free energy, what according to the result of Skrzypczyk \emph{et al.} can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and an ideal energy storage that is able to extract work from coherences. The new inequality, defined in terms of the ergotropy (rather than free energy), incorporates both of those important microsc…
The purity of quantum states is a key requirement for many quantum applications. Improving the purity is limited by fundamental laws of thermodynamics. Here we are probing the fundamental limits for a natural approach to this problem, namely heat-bath algorithmic cooling(HBAC). The existence of the cooling limit for HBAC techniques was proved by Schulman et al. in, the limit however remained unknown for the past decade. Here for the first time we find this limit. In the context of quantum thermodynamics, this corresponds to the maximum extractable work from the quantum system.
We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, that undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat mach…
The ability to perform quantum error correction is a significant hurdle for scalable quantum information processing. A key requirement for multiple-round quantum error correction is the ability to dynamically extract entropy from ancilla qubits. Heat-bath algorithmic cooling is a method that uses quantum logic operations to move entropy from one subsystem to another, and permits cooling of a spin qubit below the closed system (Shannon) bound. Gamma-irradiated, $^{13}$C-labeled malonic acid provides up to 5 spin qubits: 1 spin-half electron and 4 spin-half nuclei. The nuclei are strongly hyperf…
A method is proposed to describe Fermi or Bose systems coupled to one or several heat baths composed of fermions and/or bosons. The method, called Coupled Equations of Motion method, properly includes non-Markovian effects. The approach is exact in the Full-Coupling approximation when only bosonic particles are present in the system and baths. The approach provides an approximate treatment when fermions are present either in the system and/or in one or several environments. The new approach has the advantage to properly respect the Pauli exclusion principle for fermions during the evolution. W…
Thermodynamic Roles of Quantum Environments: From Heat Baths to Work Reservoirs
Institute of Physics, University of Freiburg（弗赖堡大学物理研究所）；Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano（米兰大学阿尔多·蓬特莫利物理系）；EUCOR Centre for Quantum Science and Quantum Computing, University of Freiburg（弗赖堡大学EUCOR量子科学与工程中心）
Pure quantum states play a central role in applications of quantum information, both as initial states for many algorithms and as resources for quantum error correction. Preparation of highly pure states that satisfy the threshold for quantum error correction remains a challenge, not only for ensemble implementations like NMR or ESR but also for other technologies. Heat-Bath Algorithmic Cooling is a method to increase the purity of set of qubits coupled to a bath. We investigated the achievable polarization by analyzing the state when no more entropy can be extracted. In particular we give an …
We consider a situation where an $N$-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general Jarzinski-type equation and conclude that heat and entropy is flowing from the hot bath to the cold one. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities. Our approach is illustrated by an analytical example. For the linear regime, i.~e., for small temperature differences b…
We study the statistics of the lasing output from a single atom quantum heat engine, which was originally proposed by Scovil and Schulz-DuBois (SSDB). In this heat engine model, a single three-level atom is strongly coupled with an optical cavity, and contacted with a hot and a cold heat bath together. We derive a fully quantum laser equation for this heat engine model, and obtain the photon number distribution for both below and above the lasing threshold. With the increase of the hot bath temperature, the population is inverted and lasing light comes out. However, we notice that if the hot b…
We consider a situation where an $N$-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation we derive general Jarzinski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.
This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics, and addresses a version of quantum heat which satisfies quantum-classical correspondence. The characteristic function and the full counting statistics of quantum heat are shown to be formally similar. The paper further shows that the method can be extended to more than one bath, e.g. two baths at different temperatures, which opens up the prospect of studying correlations and heat flow. The paper extend…
A class of autonomous quantum heat baths satisfying the eigenstate thermalization hypothesis (ETH) criteria is proposed. We show that such systems are expected to cause thermal relaxation of much smaller quantum systems coupled to one of the baths local observables. The process of thermalization is examined through residual fluctuations of local observables of the bath around their thermal values predicted by ETH. It is shown that such fluctuations perturb the small quantum system causing its decoherence to the thermal state. As an example, we investigate theoretically and numerically thermali…
We show that the case of two oscillators in a common heat bath cannot be reduced to an effective one body problem. In addition, there is an interaction between the oscillators, even at zero temperature, due to the fluctuations caused in both oscillators by the zero-point oscillations of the electromagnetic field.
We report on numerical simulations of the dynamics of a test particle coupled to competing Boltzmann heat baths of finite size. After discussing some features of the single bath case, we show that the presence of two heat baths further constraints the conditions necessary for the test particle to thermalize with the heat baths. We find that thermalization is a spectral property in which the oscillators of the bath with frequencies in the range of the test particle characteristic frequency determine its degree of thermalization. We also find an unexpected frequency shift of the test particle re…
We consider a quantum system strongly coupled to multiple heat baths at different temperatures. Quantum heat transport phenomena in this system are investigated using two definitions of the heat current, one in terms of the system energy, and the other in terms of the bath energy. When we consider correlations among system-bath interactions (CASBI) -- which have a purely quantum mechanical origin -- the definition in terms of the bath energy becomes different. We found that CASBI are necessary to maintain the consistency of the heat current with thermodynamic laws in the case of strong system-…
In this paper we investigate the relationship between the efficiency of a cyclic quantum heat engine with the Hilbert space dimension of the thermal baths. By means of a general inequality, we show that the Carnot efficiency can be obtained only when both the hot and cold baths are infinitely large. By further introducing a specific model where the baths are constituted of ensembles of finite-dimensional particles, we further demonstrate the relationship between the engine's power and efficiency, with the dimension of the working substance and the bath particles.
We provide an explicit method for solving general markovian master equations for quadratic bosonic Hamiltonians with linear bath operators. As an example we consider a one-dimensional quantum harmonic oscillator chain coupled to thermal reservoirs at both ends of the chain. We derive an analytic solution of the Redfield master equation for homogeneous harmonic chain and recover classical results, namely, vanishing temperature gradient and constant heat current in the thermodynamic limit. In the case of the disordered gapped chains we observe universal heat current scaling independent of the ba…
The optimal efficiency of quantum (or classical) heat engines whose heat baths are $n$-particle systems is given by the information geometry and the strong large deviation. We give the optimal work extraction process as a concrete energy-preserving unitary time evolution among the heat baths and the work storage. We show that our optimal work extraction turns the disordered energy of the heat baths to the ordered energy of the work storage, by evaluating the ratio of the entropy difference to the energy difference in the heat baths and the work storage, respectively. By comparing the statistic…
Within a generalized Caldeira-Leggett model we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance $r$. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a {\em microscopic} distance that is of order of the cut-off wavelength $λ$ of the system-bath interaction. At larger distances the maximal entanglement is exponentially suppressed with a decay length of order $λ$. We conclude that entanglement generation via a heat bath is not suitable …
We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajec…
We investigate the transport of phonons between $N$ harmonic oscillators in contact with independent thermal baths and coupled to a common oscillator, and derive an expression for the steady state heat flow between the oscillators in the weak coupling limit. We apply these results to an optomechanical array consisting of a pair of mechanical resonators coupled to a single quantised electromagnetic field mode by radiation pressure as well as to thermal baths with different temperatures. In the weak coupling limit this system is shown to be equivalent to two mutually-coupled harmonic oscillators…
Small systems (of interest in the areas of nanophysics, quantum information, etc.) are particularly vulnerable to environmental effects. Thus, we determine various thermodynamic functions for an oscillator in an arbitrary heat bath at arbitrary temperatures. Explicit results are presented for the most commonly discussed heat bath models: Ohmic, single relaxation time and blackbody radiation.
We calculate the exact Landau-Zener transitions probabilities for a qubit with arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of a diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
We introduce a new selected configuration interaction plus perturbation theory algorithm that is based on a deterministic analog of our recent efficient heat-bath sampling algorithm. This Heat-bath Configuration Interaction (HCI) algorithm makes use of two parameters that control the tradeoff between speed and accuracy, one which controls the selection of determinants to add to a variational wavefunction, and one which controls the the selection of determinants used to compute the perturbative correction to the variational energy. We show that HCI provides an accurate treatment of both static …
In this work, we study different quantum thermodynamic functions (QTFs) of a cold atom subjected to an artificial non-Abelian uniform magnetic field and linearly coupled to a quantum heat bath through either usual coordinate-coordinate coupling or through momentum variables. The bath is modelled as a collection of independent quantum harmonic oscillators. In each of the coupling scheme, the effect of the non-Abelian magnetic field on different QTFs are explicitly demonstrated for a U(2) gauge transformation. In each case, we show that the free energy has a different expression than that for th…
Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic resource theories to exchanges of observables other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with "grand-potential" theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law an…
Starting from the Liouville-von Neumann equation, under a weak coupling limit we derive the Lindblad master equation for the one-dimensional quantum Ising model in a Markov approximation and a rotating wave approximation. We also prove that the steady solution of the Lindblad equation is the canonical distribution independent of the dissipation rate.
