We apply the quantum trajectory method to current noise in resonant tunneling devices. The results from dynamical simulation are compared with those from unconditional master equation approach. We show that the stochastic Schrödinger equation approach is useful in modeling the dynamical processes in mesoscopic electronic systems.
By starting from the stochastic Schrödinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise quantum trajectories we use an Ornstein-Uhlenbeck coloured noise as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, we show that our non-Markovian stochastic Schrödinger equations unravel some master equations with memory kernels.
The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic Schrödinger equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact reverse stochastic Schrödinger equations admit closed-form solutions that can be implemented in real-time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modelling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.
We provide a unified view for the master equation (ME) approach and the quantum trajectory (QT) approach to the measurement problem of an electron tunnelling between two coherently coupled quantum dots (CQD’s) using a low transparency point contact (PC) or tunnel junction as a detector. We show that the master equation for the reduced or “partially” reduced density matrix can be obtained when an average or “partial” average is taken on the conditional, stochastic density matrix over the possible outcomes of the measurement. Then we simulate ) , ( t N P , the probability of finding N electron that have tunnelled through the PC in time t , using 10000 QT’s and measurement records. The simulation results of ) , ( t N P are in very good agreement with those obtained from the Fourier analysis of the “partially” reduced density matrix. The theory of QT’s (also known as stochastic Schrodinger equation or stochastic ME) has been developed in last ten years mainly in the quantum optics community to describe open quantum system subject to continuous quantum measurements. But it was introduced to the context of solid-state mesoscopics only recently (e.g., Goan et. al. 2001 and references therein). The CQD system, considered here, forms a single charge quantum bit (qubit), and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dots. The QT or stochastic quantum-jump ME of the density matrix operator ) (t c
The experimental current measured in mesoscopic systems fluctuates around average values as a consequence of the wave‐particle nature of electrons. An alternative quantum noise approach, based on Bohm trajectories, is presented. This formalism directly deals with the wave and particle nature of electrons and provides an intuitive framework to study quantum noise. The approach allows the direct consideration of coulomb correlation among electrons. In fact, most of the numerical techniques used in classical Monte Carlo simulations of electron devices can be directly adapted to our approach. Simulated noise results for interacting electrons tunnelling through double barriers are presented in agreement with experimental results. The present approach opens a new path for studying electron transport and quantum noise in mesoscopic systems.
Quantum coherent oscillations in the electric charge passing through a mesoscopic conductor can give rise to a current noise spectrum which is strongly asymmetric in frequency. The asymmetry reveals the fundamental difference between quantum and classical fluctuations in the current. We show how the quantum current noise can be obtained starting from a Born-Markov master equation, an approach which is applicable to a wide class of systems. Our method enables us to analyze the rich behavior of the current noise associated with the double Josephson quasiparticle resonance in a superconducting single-electron transistor (SSET). The asymmetric part of the noise is found to be strongly dependent on the choice of operating point for the SSET and can be either positive or negative. Our results are in good agreement with recent measurements.
We present the stochastic Schr\"odinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it to the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the environmental memory time scale, in the mean, our result recovers the solution of the known non-Lindblad quantum Brownian motion master equation. A remarkable feature of our powerful stochastic approach is its localization property: individual quantum trajectories remain localized wave packets for all times, even for the classically chaotic system considered here, the localization being stronger as $\ensuremath{\Elzxh}\ensuremath{\rightarrow}0$.