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Register a new userThe equilibrium states of open quantum systems in the strong coupling regime
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In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.
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We consider a feedback control loop rectifying particle transport through a single quantum dot that is coupled to two electronic leads. While monitoring the occupation of the dot, we apply conditional control operations by changing the tunneling rates between the dots and its reservoirs, which can be interpreted as the action of a Maxwell demon opening or closing a shutter. This can generate a current at equilibrium or even against a potential bias, producing electric power from information. While this interpretation is well-explored in the weak-coupling limit, we can address the strong-coupling regime with a fermionic reaction-coordinate mapping, which maps the system into a serial triple quantum dot coupled to two leads. There, we find that a continuous projective measurement of the central dot would lead to a complete suppression of electronic transport due to the quantum Zeno effect. In contrast, a microscopic model for the quantum point contact detector implements a weak measurement, which allows for closure of the control loop without inducing transport blockade. In the weak-coupling regime between the central dot and its leads, the energy flows associated with the feedback loop are negligible, and the information gained in the measurement induces a bound for the generated electric power. In contrast, in the strong coupling limit, the protocol may require more energy for opening and closing the shutter than electric power produced, such that the device is no longer information-dominated and can thus not be interpreted as a Maxwell demon.
The aim of the paper is to study the question whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator $cal H$. The eigenfunctions of $cal H$ contain the influence of exceptional points (EPs) as well as that of external mixing (EM) of the states via the environment. As a result, equilibrium states exist (far from EPs). They are different from those of the corresponding closed system. Their wavefunctions are orthogonal although the Hamiltonian is non-Hermitian.
We analyse dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a {em quantum level-2.5 large deviation principle} for these systems, which describes the joint fluctuations of time-averaged quantum jump rates and of the time-averaged quantum state for long times. Like its level-2.5 counterpart for classical continuous-time Markov chains (which it contains as a special case) this description is both {em explicit and complete}, as the statistics of arbitrary time-extensive dynamical observables can be obtained by contraction from the explicit level-2.5 rate functional we derive. Our approach uses an unravelled representation of the quantum dynamics which allows these statistics to be obtained by analysing a classical stochastic process in the space of pure states. For quantum reset processes we show that the unravelled dynamics is semi-Markov, and derive bounds on the asymptotic variance of the number of quantum jumps which generalise classical thermodynamic uncertainty relations. We finish by discussing how our level-2.5 approach can be used to study large deviations of non-linear functions of the state such as measures of entanglement.
The Jaynes-Cummings model, describing the interaction between a single two-level system and a photonic mode, has been used to describe a large variety of systems, ranging from cavity quantum electrodynamics, trapped ions, to superconducting qubits coupled to resonators. Recently there has been renewed interest in studying the quantum strong-coupling (QSC) regime, where states with photon number greater than one are excited. This regime has been recently achieved in semiconductor nanostructures, where a quantum dot is trapped in a planar microcavity. Here we study the quantum strong-coupling regime by calculating its photoluminescence (PL) properties under a pulsed excitation. We discuss the changes in the PL as the QSC regime is reached, which transitions between a peak around the cavity resonance to a doublet. We particularly examine the variations of the PL in the time domain, under regimes of short and long pulse times relative to the microcavity decay time.
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations between different level-crossing events can be neglected, we use the solution of the Landau-Zener problem to find how the diffusion constant depends on the noise. We also show that when an electric field or external disordered potential is applied to the system, the diffusion constant is suppressed with no drift term arising. The results are relevant to various quantum systems, including exciton diffusion in photosynthesis and electronic transport in solid-state physics.
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