Non-Ergodicity in open quantum systems through quantum feedback (original) (raw)

Non-ergodicity through quantum feedback

arXiv: Quantum Physics, 2016

Open quantum systems usually reach a unique stationary state with ergodic dynamics. In other words, the ensemble averages and the time averages of the expectation values of open quantum systems are usually the same for all quantum trajectories. Although open quantum systems are in general ergodic, many classical stochastic processes are not. Hence if classical physics emerges from microscopic quantum models, there have to be mechanisms which induce non-ergodicity in open quantum systems. In this paper, we identify such a mechanism by showing that quantum feedback dramatically alters the dynamics of open quantum systems, thereby possibly inducing non-ergodicity and a persistent dependence of ensemble averages on initial conditions. As a concrete example, we study an optical cavity inside an instantaneous quantum feedback loop.

Measurement-based quantum thermal machines with feedback control

arXiv (Cornell University), 2022

We investigate coupled-qubit-based thermal machines powered by quantum measurements and feedback. We consider two different versions of the machine: 1) a quantum Maxwell's demon where the coupled-qubit system is connected to a detachable single shared bath, and 2) a measurementassisted refrigerator where the coupled-qubit system is in contant with a hot and cold bath. In the quantum Maxwell's demon case we discuss both discrete and continuous measurements. We find that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further find that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we use continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We find that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.

Quantum thermal machines with single nonequilibrium environments

Physical Review A, 2015

We propose a scheme for a quantum thermal machine made by atoms interacting with a single non-equilibrium electromagnetic field. The field is produced by a simple configuration of macroscopic objects held at thermal equilibrium at different temperatures. We show that these machines can deliver all thermodynamic tasks (cooling, heating and population inversion), and this by establishing quantum coherence with the body on which they act. Remarkably, this system allows to reach efficiencies at maximum power very close to the Carnot limit, much more than in existing models. Our findings offer a new paradigm for efficient quantum energy flux management, and can be relevant for both experimental and technological purposes.

Nonadiabatic effects in periodically driven dissipative open quantum systems

Physical Review A, 2018

We present a general method to calculate the quasi-stationary state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) under periodic modulation of its parameters. Using Floquet's theorem, we formulate the differential equation for the system's density operator which has to be solved for a single period of modulation. On this basis we also provide systematic expansions in both the adiabatic and high-frequency regime. Applying our method to three different systems-two-and three-level models as well as the driven nonlinear cavity-we propose periodic modulation protocols of parameters leading to a temporary suppression of effective dissipation rates, and study the arising non-adiabatic features in the response of these systems.

Quantumness and memory of one qubit in a dissipative cavity under classical control

Annals of Physics

Hybrid quantum-classical systems constitute a promising architecture for useful control strategies of quantum systems by means of a classical device. Here we provide a comprehensive study of the dynamics of various manifestations of quantumness with memory effects, identified by non-Markovianity, for a qubit controlled by a classical field and embedded in a leaky cavity. We consider both Leggett-Garg inequality and quantum witness as experimentally-friendly indicators of quantumness, also studying the geometric phase of the evolved (noisy) quantum state. We show that, under resonant qubit-classical field interaction, a stronger coupling to the classical control leads to enhancement of quantumness despite a disappearance of non-Markovianity. Differently, increasing the qubit-field detuning (out-of-resonance) reduces the nonclassical behavior of the qubit while recovering non-Markovian features. We then find that the qubit geometric phase can be remarkably preserved irrespective of the cavity spectral width via strong coupling to the classical field. The controllable interaction with the classical field inhibits the effective time-dependent decay rate of the open qubit. These results supply practical insights towards a classical harnessing of quantum properties in a quantum information scenario.

Autonomous quantum thermodynamic machines

Physical review. E, Statistical, nonlinear, and soft matter physics, 2005

We investigate the dynamics of a quantum system consisting of a single spin coupled to an oscillator and sandwiched between two thermal baths at different temperatures. By means of an adequately designed Lindblad equation, it is shown that this device can function as a thermodynamic machine exhibiting Carnot-type cycles. For the present model, this means that when run as a heat engine, coherent motion of the oscillator is amplified. Contrary to the quantum computer, such a machine has a quantum as well as a classical limit. Away from the classical limit, it asymptotically approaches a stationary transport scenario.

Continual measurements for quantum open systems

Il Nuovo Cimento B Series 11, 1983

Starting from the recently introduced formalism of continual measurements in quantum mechanics, it is shown that, for the quantum open systems, it is possible to construct probability distributions for the values at all times of certain observables, without the continual measurement of such observables perturbing the dynamics of the system. )/[ore precisely, starting from the quantum description of an open system, a generalized stochastic process for certain observables is constructed, which is independent of the fact that these observables are actually measured or not. The example of the quantum Brownian motion is developed in detail. In such an example it is shown how the a priori arbitrary elements of the formalism are in reality determined by the dynamics of the system. PACS. 03.65. -Quantum theory; quantum mechanics. PACS. 02.50. -Probability theory, stochastic processes and statistics. PACS. 05.40. -Fluctuation phenomena, random processes and Brownian motion.

Non-Markovian control of qubit thermodynamics by frequent quantum measurements

Physica E-low-dimensional Systems & Nanostructures, 2010

We explore the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems (TLS), alias qubits, in contact with a thermal bath. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control of heating, cooling and statepurification (entropy reduction) of qubits, much sooner than their thermal equilibration time.

Quantum thermo-dynamical construction for driven open quantum systems

Quantum

Quantum dynamics of driven open systems should be compatible with both quantum mechanic and thermodynamic principles. By formulating the thermodynamic principles in terms of a set of postulates we obtain a thermodynamically consistent master equation. Following an axiomatic approach, we base the analysis on an autonomous description, incorporating the drive as a large transient control quantum system. In the appropriate physical limit, we derive the semi-classical description, where the control is incorporated as a time-dependent term in the system Hamiltonian. The transition to the semi-classical description reflects the conservation of global coherence and highlights the crucial role of coherence in the initial control state. We demonstrate the theory by analyzing a qubit controlled by a single bosonic mode in a coherent state.

Dynamics and Thermodynamics of Linear Quantum Open Systems

Physical Review Letters, 2013

We study the behavior of networks of quantum oscillators coupled with arbitrary external environments. We analyze the evolution of the quantum state showing that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime. We demonstrate two main results on thermodynamics: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (therefore, such refrigerators require non-linearity as a crucial ingredient, as proposed by Kosloff and others ). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities. PACS numbers: 03.65.Yz