Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExact $mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems
45
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We formulate an exact spacetime mapping between the $mathcal{N}$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A textbf{94}, 043628 (2016)] to the general case of open quantum systems with Markovian property. For this, we consider an open many-body system consisting of a $D$-dimensional quantum gas of bosons or fermions that interacts with a bath under Born-Markov approximation and evolves according to a Lindblad master equation in a regime of loss or gain. Invoking the independence of expectation values on pictures of quantum mechanics and using the quantum fields that describe the gas dynamics, we derive the Heisenberg evolution of any arbitrary $mathcal{N}$-point function of the system in the regime when the Lindblad generators feature a loss or a gain. Our quantum field mapping for closed quantum systems is rewritten in the Schrodinger picture and then extended to open quantum systems by relating onto each other two different evolutions of the $mathcal{N}$-point functions of the open quantum system. As a concrete example of the mapping, we consider the mean-field dynamics of a simple dissipative quantum system that consists of a one-dimensional Bose-Einstein condensate being locally bombarded by a dissipating beam of electrons in both cases when the beam amplitude or the waist is steady and modulated.
rate research
Read More
Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact solutions. Here we present an exact result which holds even when no exact solutions can be found: a class of spacetime mappings of different experiments onto each other, as long as the gas particles interact via two-body potentials which possess a scaling property that most real interactions do possess. Since our result is an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics, it is otherwise general; it applies to arbitrary measurements on any mixtures of Bose or Fermi gases, in arbitrary initial states. Practical applications of this mapping include perfect simulation of non-trivial experiments with other experiments which may be easier to perform.
The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $ntoinfty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $ntoinfty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.
We introduce jumptime unraveling as a distinct method to analyze quantum jump trajectories and the associated open/continuously monitored quantum systems. In contrast to the standard unraveling of quantum master equations, where the stochastically evolving quantum trajectories are ensemble-averaged at specific times, we average quantum trajectories at specific jump counts. The resulting quantum state then follows a discrete, deterministic evolution equation, with time replaced by the jump count. We show that, for systems with finite-dimensional state space, this evolution equation represents a trace-preserving quantum dynamical map if and only if the underlying quantum master equation does not exhibit dark states. In the presence of dark states, on the other hand, the state may decay and/or the jumptime evolution eventually terminate entirely. We elaborate the operational protocol to observe jumptime-averaged quantum states, and we illustrate the jumptime evolution with the examples of a two-level system undergoing amplitude damping or dephasing, a damped harmonic oscillator, and a free particle exposed to collisional decoherence.
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The investigation of open systems mostly relies on exact diagonalization of the Liouville superoperator or quantum trajectories. In this approach, the system size is rather limited by current computational capabilities. Analogous to closed-system PT, we develop a PT suitable for open quantum systems. This proposed method is useful in the analytical understanding of open systems as well as in the numerical calculation of system properties, which would otherwise be impractical.
Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in condensed matter. This concerns both their non-thermal flux equilibrium states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
