Search

We study a limit cycle of a quantum Otto engine whose each cycle consists of two finite-time quantum isochoric (heating or cooling) processes and two quantum adiabatic work-extracting processes. Considering a two-level system as a working substance that weakly interacts with two reservoirs comprising an infinite number of bosons, we investigate the non-Markovian effect (short-time behavior of the reduced dynamics in the quantum isochoric processes (QIPs)) on work extraction after infinite repetition of the cycles. We focus on the parameter region where energy transferred to the reservoir can come back to the system in a short-time regime, which we call energy backflow to show partial quantum-mechanical reversibility. As a situation completely different from macroscopic thermodynamics, we find that the interaction energy is finite and negative by evaluating the average energy change of the reservoir during the QIPs by means of the full-counting statistics, corresponding to the two-point measurements. The feature leads us to the following findings: (1) the Carnot theorem is consistent with a definition of work including the interaction energy, although the commonly used definition of work excluding the interaction leads to a serious conflict with the thermodynamic law, and (2) the energy backflow can increase the work extraction. Our findings show that we need to pay attention to the interaction energy in designing a quantum Otto engine operated in a finite time, which requires us to include the non-Markovian effect, even when the system-reservoir interaction is weak., Comment: 13pages, 7 figures

We proposed the finite-time cycle model of a measurement-based quantum cooler, where invasive measurement provides the power to drive the cooling cycle. Such a cooler may be regarded as an alternative thought experiment of Mawell's demon. The measurement-feedback information is capable of moving heat from the cold to hot bath without any work input and even making the maximum coefficient of performance larger than the Carnot limit. The causes that this seemingly paradoxical result does not violate the laws of thermodynamics can be clearly explained through the derivation of a generalized Clausius inequality including the mutual information.

Landauer's principle provides a perspective on the physical meaning of information as well as on the minimum working cost of information processing. Whereas most studies have related the decrease in entropy during a computationally irreversible process to a lower bound of dissipated heat, recent efforts have also provided another lower bound associated with the thermodynamic fluctuation of heat. The coexistence of the two conceptually independent bounds has stimulated comparative studies of their close relationship or tightness; however, these studies were concerned with finite quantum systems that allowed the revival of erased information because of a finite recurrence time. We broaden these comparative studies further to open quantum systems with infinite recurrence times. By examining their dependence on the initial state, we find the independence of the thermodynamic bound from the initial coherence, whereas the entropic bound depends on both the initial coherence and the population. A crucial role is indicated by the purity of the initial state: The entropic bound is tighter when the initial condition is sufficiently mixed, whereas the thermodynamic bound is tighter when the initial state is close to a pure state. These trends are consistent with previous results obtained for finite systems.

Transport phenomena are ubiquitous throughout the science, engineering and technology disciplines as it concerns energy, mass, charge and information exchange between systems. In particular, energy transport in the nanoscale regime has attracted significant attention within the physical science community due to its potential to explain complex phenomena like the electronic energy transfer in molecular crystals or the Fenna-Matthews-Olson / light harvesting complexes in photosynthetic bacteria with long time coherences. Energy transport in these systems is highly affected by environmental noise but surprisingly not always in a detrimental way. It was recently found that situations exist where noise actually enhances the transport phenomena. Such noise can take many forms, but can be characterised in three basic behaviours: quantum, coloured or nonlocal. All have been shown potential to offer an energy transport enhancement. The focus of this work is on quantum transport caused by stochastic environment with spatio-temporal correlation. We consider a multi-site nearest neighbour interaction model with pure dephasing environmental noise with coloured and nonlocal character and show how an accelerated rate for the energy transfer results especially under anti-correlation. Negative spatial correlations provide another control parameter to help one establish the most efficient transfer of energy and may provide new insights into the working of exciton transport in photosynthetic complexes. Further the usage of spatio-temporal correlated noise may be a beneficial resource for efficient transport in large scale quantum networks., 11 pages 5 figures

The miniaturization of spintronic devices, specifically, nanoscale devices employing spintronics, has attracted intensive attention from a scientific as well as engineering perspective. In this paper, we study a non-Markovian effect on spin pumping to describe spin current generation driven by the magnetization of arbitrary precession frequency in a quantum dot attached to an electron lead. Although the Markovian approximation can be used when driving is sufficiently slow compared with relaxation times in electron tunneling, recent developments in nanospintronic devices show that we need to include non-Markovian effects. In contrast to the one-way-only nature of the spin current generation under Markovian dynamics, we find that non-Markovian dynamics exhibit a temporal backflow of spin, called spin backflow for brevity. We capture the phenomenon by introducing its quantifier, and show that the backflow reduces the amount of spin current significantly when the frequency exceeds the relaxation rate. This prevents an unphysical divergence of the spin current in the high-frequency limit that occurs under the Markovian approximation. We believe our analysis provides an understanding of the spin pumping particularly in regard to producing a more efficient spin current generation over shorter time scales by going beyond the conventional Markovian approximation.

We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the full counting statistics formalism, which we use to evaluate the first moment of its probability distribution. We focus in particular on the energy backflow from environment to system, to which we associate a suitable condition and quantifier, which enables us to draw a connection with a recently introduced notion of non-Markovianity based on information backflow. This quantifier is then studied in detail in the case of the spin-boson model, described within a second order time-convolutionless approximation, observing that non-Markovianity allows for the observation of energy backflow. This analysis allows us to identify the parameters region in which energy backflow is higher., Comment: 11 pages, 5 figures; published version

The authors have studied the excitons and excitonic complexes in two kinds of self-assembled quantum dots (QDs) using photon echo measurements. In GaAs strain-induced quantum dots (SIQDs), a pronounced biexcitonic beat with a period of 1 ps is observed. The biexciton binding energy in SIQDs is obtained from the beat period, and its magnetic field dependence is investigated. It is found that the biexciton binding energy is remarkably increased by the lateral confinement and they are almost independent of the applied magnetic field up to 8 T. A theoretical calculation of the biexciton binding energy in SIQDs is presented to explain the observed magnetic field dependence. In charge-tunable InP QDs, the photon echo signal shows dramatic changes depending on the electric bias. The decay profile of the echo intensity is not a single exponential but Gaussian-like function, which indicates non-Markovian nature of the dephasing process in this system. Theoretical calculation is done assuming tunneling induced dephasing mechanism, and it reproduces the experimental results quite well.

Non-Markovian dynamical maps are derived by using the projection operator method in Hilbert–Schmidt space. The eigenvalues and eigenvectors of the obtained maps describe the relaxation processes. We found that a dynamical map for a spin-bath model periodically becomes positive but not completely positive by the non-Markovian effect of the system–reservoir interaction.

A highly sensitive heterodyne-detected photon echo enabled us to observe the signal from one layer of neutral self-assembled InP quantum dots under an electric field. The photon echo signal dramatically increased when charged InP quantum dots were neutralized with the application of negative electric bias. This fact suggests the hypothesis that charged quantum dots do not produce the photon echo. With the further increase of negative electric bias, photoluminescence was quenched and the photon echo decayed faster. The photon echo showed tunneling-induced dephasing and decayed nonexponentially, reflecting the non-Markovian nature of the tunneling process.

We observed the tunneling process of photo-excited holes in neutral InP quantum dots and Pauli blocking of charged InP quantum dots. A highly sensitive heterodyne-detected photon echo method enabled us to observe the signal from one layer of self-assembled InP quantum dots under the electric field. The electric field could control the charging or neutralization of the InP quantum dots and hence the photon echo signal decreased considerably with the increase of electron doping. The photon echo of neutral InP quantum dots under the electric field showed tunneling-induced dephasing, which decays non-exponentially reflecting the non-Markovian nature of the tunneling process.

We discuss the effectiveness of the multipulse control on the spin-boson model where a spin nonlinearly interacts with a boson reservoir. We find the multipulse control is effective when the pulse interval is sufficiently shorter than the correlation time of the system-reservoir interaction. Moreover, the pure dephasing can also be suppressed by paying attention to the dynamical motion of the reservoir.

We provide a general formula of quantum transfer that includes the non-adiabatic effect under periodic environmental modulation by using full counting statistics in Hilbert-Schmidt space. Applying the formula to an anharmonic junction model that interacts with two bosonic environments within the Markovian approximation, we find that the quantum transfer is divided into the adiabatic (dynamical and geometrical phases) and non-adiabatic contributions. This extension shows the dependence of quantum transfer on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequency of spectral density. We show that the non-adiabatic contribution represents the reminiscent effect of past modulation including the transition from the initial condition of the anharmonic junction to a steady state determined by the very beginning of the modulation. This enables us to tune the frequency range of modulation, whereby we can obtain the quantum flux corresponding to the geometrical phase by setting the initial condition of the anharmonic junction., Comment: 11 pages, 4 figures; mistypes are corrected

The formation of the atomic coherence via a photon field has been considered to play an essential role in the laser action. The importance of the formation has been also recognized from the viewpoint of cavity QED. This paper analyzes quantum mechanical dynamics of a self-organized formation of coherence between atoms and photon field. We solved an equation of a reduced density operator for a quantum laser model with plural atoms by using coherent states and orthogonal polynomials, and obtained a solution in a continued fraction form. We numerically evaluate time evolution of averaged physical quantities and quasi-probability density of photon field. Under an appropriate condition for laser oscillation, time evolution of an average of induced atomic dipole moments shows a co-operative phenomenon. Numerical evaluation of the quasi-probability density of a photon field reveals that a coherently more stabilized and stronger photon field emerges as the number of atoms increases. To our knowledge, this is the ...

We formulate a quantum statistical mechanical theory of relaxation for a spin 1/2 system interacting with a quantum environment. Our theory has the advantage compared to previous ones in simultaneously treating both (i) arbitrary modulation speed (and/or any strength of modulation) of the fluctuating field and (ii) any temperature region of the environment.

A systematic damping theoretical formalism is presented to give basic equations of statistical physics. Our formalism naturally yields the so-called time convolution (TC) and time convolutionless (TCL) equations both for a density matrix and for dynamical variables. The method is explicitly used to obtain equations in the Heisenberg picture (equations of motion for dynamical variables). In contrast to the existing derivation of equations of motion, the present formalism gives a systematic method for deriving these equations without specifying the projection operator. Moreover, the formalism is valid even for time-dependent Hamiltonian systems. A simple example is given to illustrate our formalism.

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal polynomials. The expansion coefficients are solved to give a continued fraction. A complete solution is obtained, namely, time evolution of the probability density is determined as well as that for certain physical quantities. The solution is valid even for strong coupling between photons and atoms: it is free from restriction on system parameters. Detailed studies on dynamics are performed for typical values of the system parameters. This is a prototype of interacting quantum nonequilibrium systems. Relevance to systems other than a laser is briefly mentioned.

A mathematical correspondence is established between a set of equations due to Mori formalism and those of generalized tri-diagonal recurrence relations. Thus, once a set of coupled equations describing physical phenomena are given, the corresponding Langevin equations can be obtained directly. This enables us to construct a hierarchical structure of physical variables and time scales

We demonstrate that local application of a weak external field increases distinguishability between states with and without initial correlations. We consider the case where a two-level system linearly and adiabatically interacts with an infinite number of bosons. We evaluate the trace distance (or, equivalently, the Hilbert-Schmidt distance) between the quantum states which evolve from two kinds of initial states; the correlated Gibbs state and its uncorrelated marginal state. We find that the trace distance increases above its initial value for any and all parameter settings. This indicates that we can explore the existence of initial system-environment correlations with applying a local external field, which causes the breakdown of the contractivity., Comment: 7 pages, 4 figures

A model of quantum dynamics of nonadiabatic transition in energy crossing two-level systems (Landau-Zener model) with fluctuation and dissipation mechanisms is formulated on the basis of the damping theory. The model is composed of a two-level system interacting with a single-mode boson system which is surrounded by a reservoir. The basic equation which describes time-evolution of the relevant system is transformed into bitridiagonally coupled differential equations which are solved numerically. Characteristics of our formulation are the following. It is possible to study the quantum dynamics at any temperature and to treat a situation when the fluctuation field is strong. This is because our theory is extended beyond the applicability of the usual perturbation theory. Moreover, our theory can treat both the diagonal and the off-diagonal fluctuations simultaneously.

An extended version of a quantum statistical mechanical laser model is solved rigorously. With the use of coherent states and orthogonal polynomials, the original equation is solved to give a continued fraction. The average of the induced atomic dipole moment is evaluated to give the cooperative rotational motion.

A microscopic quantum statistical laser model, a prototype of a non-equilibrium open system, is solved regorously [1]. With an extension to the two-atom system and the intuitive discussion based on the photon elimination [2], the origin of the atomic coherence in the laser medium is also discussed.

Numerical evaluations of path integrals are done for a stochastic model of spin relaxation based on a previous formulation. Explicitly, with the use of stochastic differential equations, the path integrals with respect to the stochastic fluctuating field are performed by a generalized version of the Runge-Kutta method. The computational results are compared with the known exact analytic solutions and fully numerical calculations. The path integral solution is shown to be satisfactory.

A microscopic laser equation is solved rigorously. In order to transform the original equation of the density matrix into a more tractable partial differential equation, spin and boson coherent states are used. The resulting equation for the probability density is solved to give a continued fraction with the use of orthogonal polynomials. As a preliminary result, dynamics of certain physical quantities are calculated.

A rigorous solution is found for a basic equation which determines the time evolution of the nonlinear spin relaxation process. Spin coherent representation is used to transform an original operator equation into a Fokker-Planck-type c -number equation for the probability density which is expanded in terms of spherical harmonics. Then the expansion coefficients are completely determined in the form of a continued fraction. Relevant averages such as moments and cumulants are calculated.

The linear transient response of a two-level system coupled with an environmental system is studied under correlated and factorized initial conditions. We find that the transient response in these cases differs significantly from each other, especially for strong system-environment interaction at intermediate temperatures. This means that it is necessary to pay attention to the initial conditions chosen when analyzing experiments on transient linear response, because the conventional factorized initial condition results in an incorrect response, in which the quantum correlation between the relevant system and the environmental system is disregarded., 4 pages, 4 figures, typos are corrected, to be appeared in PRA

Relation among various expressions of the complex admittance for quantum systems in contact with heat reservoir is studied. Exact expressions of the complex admittance are derived in various types of formulations of equations of motion under contact with heat reservoir. Namely, the complex admittance is studied in the relaxation method and the external-field method. In the former method, the admittance is calculated using the Kubo formula for quantum systems in contact with heat reservoir in no external driving fields, while in the latter method the admittance is directly calculated from equations of motion with external driving terms. In each method, two types of equation of motions are considered, i.e., the time-convolution (TC) equation and time-convolutionless (TCL) equation. That is, the full of the four cases are studied. It is turned out that the expression of the complex admittance obtained by using the relaxation method with the TC equation exactly coincides with that obtained by using the external-field method with the TC equation, while other two methods give different forms. It is also explicitly demonstrated that all the expressions of the complex admittance coincide with each other in the lowest Born approximation for the systemreservoir interaction. The formulae necessary for the higher order expansions in powers of the system-reservoir interaction are derived, and also the expressions of the admittance in the n-th order approximation are given. To characterize the TC and TCL methods, we study the expressions of the admittances of two exactly solvable models. Each exact form of admittance is compared with the results of the two methods in the lowest Born approximation. It is found that depending on the model, either of TC and TCL would be the better method., 34pages, no figure

We propose a formulation to obtain the line shape of a magnetic response with dissipative effects that directly reflects the nature of the environment. Making use of the fact that the time evolution of a response function is described by the same equation as the reduced density operator, we formulate a full description of the complex susceptibility. We describe the dynamics using the equation of motion for the reduced density operator, including the term for the initial correlation between the system and a thermal bath. In this formalism, we treat the full description of non-Markovian dynamics, including the initial correlation. We present an explicit and compact formula up to the second order of cumulants, which can be applied in a straightforward way to multiple spin systems. We also take into account the frequency shift by the system-bath interaction. We study the dependence of the line shape on the type of interaction between the system and the thermal bath. We demonstrate that the present formalism is a powerful tool for investigating various kinds of systems, and we show how it is applied to spin systems, including those with up to three spins. We distinguish the contributions of the initial correlation and the frequency shift, and make clear the role of each contribution in the Ohmic coupling spectral function. As examples of applications to multispin systems, we obtain the dependence of the line shape on the spatial orientation in relation to the direction of the static field (Nagata-Tazuke effect), including the effects of the thermal environment, in a two-spin system, along with the dependence on the arrangement of a triangle in a three-spin system., Comment: 12 Figures, to be appeared in Physical Review E Typos are corrected

In this study, we provide a way to describe the dynamics of quantum tomography in an open system with a generalized master equation, considering a case where the relevant system under tomographic measurement is influenced by the environment. We apply this to spin tomography because such situations typically occur in μSR (muon spin rotation/relaxation/resonance) experiments where microscopic features of the material are investigated by injecting muons as probes. As a typical example to describe the interaction between muons and a sample material, we use a spin-boson model where the relevant spin interacts with a bosonic environment. We describe the dynamics of a spin tomogram using a time-convolutionless type of generalized master equation that enables us to describe short time scales and/or low-temperature regions. Through numerical evaluation for the case of Ohmic spectral density with an exponential cutoff, a clear interdependency is found between the time evolution of elements of the density operator and a spin tomogram. The formulation in this paper may provide important fundamental information for the analysis of results from, for example, μSR experiments on short time scales and/or in low-temperature regions using spin tomography.

It is known that a quantum system with finite degrees of freedom can simulate a composite of a system and an environment if the state of the hypothetical environment is randomized by external manipulation. We show theoretically that any phase decoherence phenomena of a single qubit can be simulated with a two-qubit system and demonstrate experimentally two examples: one is phase decoherence of a single qubit in a transmission line, and the other is that in a quantum memory. We perform NMR experiments employing a two-spin molecule and clearly measure decoherence for both cases. We also prove experimentally that the bang-bang control efficiently suppresses decoherence., Comment: 25 pages, 7 figures; added references

application/pdf, We observed the tunneling induced dephasing and Pauli blocking in InP quantum dots (QDs). A highly-sensitive heterodyne-detected photon echo method enabled us to observe the signal from one layer of self-assembled InP QDs in charged or neutral condition controlled by the electric field. The photon echo signal decreased much with the increase of electron doping. The photon echo of neutral InP QDs under the electric field showed tunneling-induced dephasing, which decays non-exponentially reflecting the non-Markovian nature of the tunneling process.

We present a new strategy for multipulse control over decoherence. When a two-level system interacts with a reservoir characterized by a specific frequency, we find that the decoherence is effectively suppressed by synchronizing the pulse-train application with the dynamical motion of the reservoir., 14 pages, 8 figures

We present a general formulation to suppress pure dephasing by multipulse control. The formula is free from a specific form of interaction and is expressed in terms of the correlation function of arbitrary system-reservoir interaction., Comment: 9 pages, 9 figures,REVTeX style; added 1 section in appendix, added references in section 1

The method of projection operators, which plays an important role in the field of nonequilibrium statistical mechanics, has been established with the use of the Liouville--von Neumann equation for a density matrix to eliminate irrelevant information from a whole system. We formulate a unified and general projection operator method for dynamical variables. The main features of our formalism parallel those for the Liouville--von Neumann equation. (1) Two types of basic equations, time-convolution and time-convolutionless decompositions, are systematically obtained without specifying a projection operator. (2) Expansion formulas for both decompositions are also obtained. (3) Problems incorporating a time-dependent Liouville operator can be flexibly treated. We apply the formulas to problems in random frequency modulation and low field resonance. In conclusion, our formalism yields a more direct and easier means of determining the average time evolution of an operator than the one for the Liouville--von Neumann equation.

Dielectric relaxation phenomena are analyzed with an exactly solvable model. This is such a general model that it includes typical stochastic processes and models as special cases. The solutions in the frequency domain as well as in the time domain are obtained and dielectric function e(ω) is explicitly calculated.

Dielectric relaxation theory is formulated taking into account the effect of inertia and the memory effect. With the use of the damping theoretical expansion formula, a rigorous equation for the probability density is derived and solved exactly in terms of the Jacobi theta function. Dielectric absorption, dispersion and fluctuation of the dipole moment are determined. For higher frequencies (i.e. short time behavior), deviation from the Debye result is found and the relevance to experiments is discussed.