Quantum trajectories and open many-body quantum systems

By Andrew J. Daley. 2014

817 citations recorded by the source corpus.

The study of open quantum systems – microscopic systems exhibiting quantum coherence that are coupled to their environment – has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This method was developed in quantum optics as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. In this article, we review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods in these systems. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/974de3d89fac673858ab08fb9123ef3417f601fd

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In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. V. Khemani
3. Matthew Fisher
4. I. Bloch
5. Andrew J. Daley
6. S. Diehl
7. Darrick E. Chang
8. Franco Nori

Citations in the corpus

• Subradiant states of quantum bits coupled to a one-dimensional waveguide (2018, background): “Their interpretation as shifts and decay rates can be understood from the equivalent quantum jump interpretation [32] of the master equation (1).”
• Microscopic Control and Detection of Ultracold Strontium in Optical-Tweezer Arrays (2018, background): “dynamics associated with the spin and motional degreesof-freedom when driving the (1)S0 ↔ (3)P1 transition [24, 67, 75].”
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories (2020, background): “Such instantaneous switching caused by quantum jumps is fundamental to obtain a theory of the system-environment interaction consistent with a probabilistic interpretation of quantum-mechanical measurements [20,21,27,28].”
• Keldysh field theory for driven open quantum systems (2015, methodology): “On the numerical side, progress has been made in one spatial dimension recently by combining the method of quantum trajectories with powerful density matrix renormalization group algorithms [87–90], see [48] for an excellent review on the topic.”
• Nonlinear waves in PT -symmetric systems (2016, background): “This phenomena can be termed to as macroscopic Zeno effect (Shchesnovich and Konotop, 2010) which is a macroscopic (meanfield) manifestation of the well-known quantum Zeno effect (Daley, 2014; Facchi and Pascazio, 2008).”
• Lattice gauge theory simulations in the quantum information era (2016, methodology): “Once the tensor network ansatz of the state is chosen, a whole family of algorithm, polynomially in the system size N , can be developed to study the properties of system under study within this approximation: one has access to the ground state properties and the time evolution determined by the tim”
• Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “Figure 9(a) sketches a quantum trajectory associated with the QME Eq.”
• Random Quantum Circuits (2022, background): “the Bloch sphere, with measurements causing “quantum jumps” (99, 100, 101, 102, 103, 104) to the North or South pole (Sec.”
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps (2019, background): “Quantum trajectories describe a system whose environment is continuously and perfectly probed [8,9,12,14,36].”