Dissipative Quantum Systems Research Articles

Dynamical Steady States in Driven Quantum Systems

We derive dynamical equations for a driven, dissipative quantum system in which the environment-induced relaxation rate is comparable to the Rabi frequency, avoiding assumptions on the frequency dependence of the environmental coupling. When the environmental coupling varies significantly on the scale of the Rabi frequency, secular or rotating wave approximations break down. We avoid these approximations, yielding dynamical steady states which account for the interaction between driven quantum dots and their phonon environment. The theory, which is motivated by recent experimental observations, qualitatively and quantitatively describes the transition from asymmetric unsaturated resonances at weak driving to population inversion at strong driving.

Energy Minimization Problem in Two-Level Dissipative Quantum Control: Meridian Case

We analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky–Lindblad equation. According to the Pontryagin maximum principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous analysis from [5] concerning 2D solutions in the case where the Hamiltonian dynamics are integrable.

Quench dynamics of a dissipative quantum system: A renormalization group study

We study dissipation in a small quantum system coupled to an environment held in thermodynamic equilibrium. The relaxation dynamics of a system subject to an abrupt quench in the parameters of the underlying Hamiltonian is investigated using two complementary renormalization group approaches. The methods are applied to the Ohmic spin-boson model close to the coherent-to-incoherent transition. In particular, the role of non-Markovian memory for the relaxation before and after the quench of the spin-boson coupling and the Zeeman splitting of the up and down spin is investigated.

Quantum Process Tomography Quantifies Coherence Transfer Dynamics in Vibrational Exciton

Quantum coherence has been a subject of great interest in many scientific disciplines. However, detailed characterization of the quantum coherence in molecular systems, especially its transfer and relaxation mechanisms, still remains a major challenge. The difficulties arise in part because the spectroscopic signatures of the coherence transfer are typically overwhelmed by other excitation-relaxation processes. We use quantum process tomography (QPT) via two-dimensional infrared spectroscopy to quantify the rate of the elusive coherence transfer between two vibrational exciton states. QPT retrieves the dynamics of the dissipative quantum system directly from the experimental observables. It thus serves as an experimental alternative to theoretical models of the system-bath interaction and can be used to validate these theories. Our results for coupled carbonyl groups of a diketone molecule in chloroform, used as a benchmark system, reveal the nonsecular nature of the interaction between the exciton and the Markovian bath and open the door for the systematic studies of the dissipative quantum systems dynamics in detail.

Dividing Line between Quantum and Classical Trajectories in a Measurement Problem: Bohmian Time Constant

This Letter proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the dividing line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schrödinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant that should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8×10(-15) m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i.e., τ(Bmax)=10(-26) s.

Hartman effect and dissipative quantum systems

The dwell time for dissipative quantum system is shown to increase with barrier width. It clearly precludes Hartman effect for dissipative systems. Here calculation has been done for inverted parabolic potential barrier.

Parallel computations of dissipative quantum systems: A nonlinear oscillator in a strict quantum regime

A software package for the numerical study of quantum dissipative systems in the field of photonics and quantum optics is developed in a cluster that includes the graphical user interface. Library of C++ classes for numerical simulation of the time evolution of the density matrix, the mean values of different operators (the mean number of photons, the correlation functions of various orders, quadratic mean fluctuations, etc.), the Poincare section, and various quasi-probability distribution functions including the Wigner function in phase space is created. As an application, the results of calculations for a nonlinear oscillator in a strict quantum regime are obtained.

Oscillatory Dynamics and Non-Markovian Memory in Dissipative Quantum Systems

The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (i) the oscillatory dynamics close to a coherent-to-incoherent transition is significantly different from the one of the classical damped harmonic oscillator and that (ii) non-Markovian memory plays a prominent role in the time evolution after a quantum quench.

Nonperturbative stochastic method for driven spin-boson model

We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that describes a two-level system interacting with a bosonic bath of harmonic oscillators. This model is archetypal for investigating dissipation in quantum systems, and tunable experimental realizations exist in mesoscopic and cold-atom systems. It finds abundant applications in physics ranging from the study of decoherence in quantum computing and quantum optics to extended dynamical mean-field theory. Starting from the real-time Feynman-Vernon path integral, we derive an exact stochastic Schr\"odinger equation that allows us to compute the full spin density matrix and spin-spin correlation functions beyond weak coupling. We greatly extend our earlier work [P. P. Orth, A. Imambekov, and K. Le Hur, Phys. Rev. A 82, 032118 (2010)] by fleshing out the core concepts of the method and by presenting a number of interesting applications. Methodologically, we present an analogy between the dissipative dynamics of a quantum spin and that of a classical spin in a random magnetic field. This analogy is used to recover the well-known noninteracting-blip approximation in the weak-coupling limit. We explain in detail how to compute spin-spin autocorrelation functions. As interesting applications of our method, we explore the non-Markovian effects of the initial spin-bath preparation on the dynamics of the coherence ${\ensuremath{\sigma}}^{x}(t)$ and of ${\ensuremath{\sigma}}^{z}(t)$ under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of ${\ensuremath{\sigma}}^{z}(t)$ without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at nonzero bias and different temperatures.

Non-Markovianity and Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality violation in quantum dissipative systems

We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay rate, λ(c) for select partitions. We discuss the applicability of these results to photosynthetic systems.

Stochastic process behind nonlinear thermodynamic quantum master equation. II. Simulation

We simulate a piecewise deterministic Markovian jump process that represents an unraveling of a nonlinear quantum master equation describing the evolution of a quantum subsystem in contact with a heat bath. This process relies on running ensemble averages and state vectors normalized only on average. The latter causes the normalization of a small subset of trajectories to grow exponentially, resulting in numerical instability. We propose an efficient solution to this problem and illustrate the general ideas for a harmonic oscillator and a two-level system, each of them being weakly coupled to a heat reservoir. Our findings lay the foundation for a powerful simulation technique for dissipative quantum systems surrounded by general classical nonequilibrium environments.

Spontaneous supersymmetry breaking induced by vacuum condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon a ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial role in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess–Zumino model, that can be considered as an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.

C*-geometric phase for mixed states: entanglement, decoherence and the spin system

We study a kind of geometric phase for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and dissipative quantum systems which uses a C*-module structure. We show that the system presents, from the viewpoint of their geometric phases, two behaviours. The first one is identical to the behaviour of an isolated spin driven by a magnetic field, as the problem originally treated by Berry. The second one is specific to the decoherence process. The gauge structures induced by these geometric phases are then similar to a magnetic monopole gauge structure for the first case, and can be viewed as a kind of instanton gauge structure for the second case. We study the role of these geometric phases in the evolution of a mixed state, particularly by focusing on the evolution of the density matrix coherence. We investigate also the relation between the geometric phase of the mixed state of one of the entangled systems and the geometric phase of the bipartite system.

Electronic resonances on a metal surface associated with adsorption

Physical aspects of the nature of chemical bonding of halogenide anions with the surface of a metal electrode during specific adsorption from electrolyte solution were considered on a qualitative level. It was shown that a description of a typical dissipative quantum system (adsorbate-substrate) can be approximated by the one-electron mechanism of bonding, allowing stationary fractional separation of the electron charge density between the atomic core of the anion and metal. Partial charge transfer from anion to metal is due to the tunneling permeability of potential barrier separating the quasi-stationary state of valent electron in the anion from free electron states in the metal. The local volume density of this charge is formed as a result of potential scattering of electron waves of metal on an anion atomic core and is concentrated near the inner surface in the vicinity of the scattering center. The residual charge of the adsorbed anion is supported by resonant scattering on the atomic core of electron waves of occupied electron states of the metal from the vicinity of the Fermi boundary. Conservation of the total charge is guaranteed by the Friedel sum rule. A physical model was used to interpret the patterns observed in the data of electrosorption valency measurements.

Quantum Isoperiodic Stable Structures and Directed Transport

It has been recently found that the so-called isoperiodic stable structures (ISSs) have a fundamental role in the classical current behavior of dissipative ratchets [Phys. Rev. Lett. 106, 234101 (2011).]. Here I analyze their quantum counterparts, the quantum ISSs (QISSs), which have a fundamental role in the quantum current behavior. QISSs have the simple attractor shape of those ISSs which settle down in short times. However, in the majority of the cases they are strongly different from the ISSs, looking approximately the same as the quantum chaotic attractors that are at their vicinity in parameter space. By adding thermal fluctuations of the size of ħ(eff) to the ISSs I am able to obtain very good approximations to the QISSs. I conjecture that in general, quantum chaotic attractors could be well approximated by means of just the classical information of a neighboring ISS plus thermal fluctuations. I expect to find this behavior in quantum dissipative systems in general.

Nonlocal dissipative tunneling for high-fidelity quantum-state transfer between distant parties

In this work, we propose the nonlocal tunneling mechanism for high-fidelity state transfer between distant parties. The nonlocal tunneling follows from the overlap between the distant sending and receiving wave functions, which is indirectlymediated by the off-resonant normal modes of a quantum channel. This channel is made up of a network of dissipative quantum systems exhibiting the same bosonic or fermionic statistical nature as the sender and receiver. We demonstrate that the incoherence arising from quantum channel nonidealities is almost completely circumvented by the tunneling mechanism, which thus affords a high-fidelity transfer process.

Heavy quarkonia in a medium as a quantum dissipative system: master-equation approach

The problem of the evolution of a heavy quarkonium in a medium can be recast as that of a quantum dissipative system. Within the framework of the master-equation approach to open quantum systems, we consider the real-time dynamics of quarkonia. We find that in a plasma at fixed temperature, the populations of the various quarkonium states evolve together, while their momentum distribution satisfies a Fokker-Planck equation.

The Observables of a Dissipative Quantum System

A time-dependent product is introduced between the observables of a dissipative quantum system, that accounts for the effects of dissipation on observables and commutators. In the t → ∞ limit this yields a contracted algebra. This product can be transported back by duality on the space of states. The general ideas are corroborated by a few explicit examples.

Role of environment and confinement in quantum dissipative dynamics: A pedestrian approach

In this paper, the long time and short time behavior of a free quantum Brownian particle and of a quantum harmonic oscillator coupled to a quantum heat bath is investigated for different spectral density functions. Not only are the usual Ohmic, Drude or radiation heat bath schemes employed to derive explicit expressions for the generalized susceptibility χ(t) and the position correlation function σ(t) but also the most intriguing frequency dependent heat bath spectra are considered. Emphasis is laid on the dependence on the low-frequency behavior but in some cases also the high-frequency cutoff becomes relevant. The present investigation also sheds light on the role of boundary in long time and short time behavior of quantum dissipative systems.

Time-dependent Markovian master equation for adiabatic systems and its application to Cooper-pair pumping

For adiabatically and periodically manipulated dissipative quantum systems we derive, using Floquet theory, a simple Markovian master equation. Contrary to some previous works we explicitly take into account the time dependence of the Hamiltonian and, therefore, obtain a master equation with a time-dependent dissipative part. We illustrate our theory with two examples and compare our results with the previously proposed master equations. In particular, we consider the problem of Cooper pair pumping and demonstrate the inadequacy of the secular (rotating wave) approximation when calculating the pumped charge. The secular approximation producing a master equation of the Lindblad type approximates well the quantum state (density matrix) of the system, while to determine the pumped charge a non-Lindblad master equation beyond the rotating wave approximation is necessary.