Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit

• URL: http://arxiv.org/abs/2012.01196v3
• Date: Mon, 28 Dec 2020 08:52:35 GMT
• Title: Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit
• Authors: Varun Dubey and Cedric Bernardin and Abhishek Dhar
• Abstract summary: The time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol. For a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian. As a specific example we consider the evolution of a quantum particle on a one-dimensional lattice that is subjected to position measurements at a specific site. By solving the corresponding non-Hermitian wave function evolution equation, we present analytic closed-form results on the survival probability and the first arrival time distribution. Finally we discuss the limit of vanishing lattice spacing and show that this leads to a continuum description where the particle evolves via the free Schrodinger equation with complex Robin boundary conditions at the detector site. Several interesting physical results for this dynamics are presented.

Related papers

• A non-Hermitian loop for a quantum measurement [0.0]
  We establish a framework for a mechanism steering state vector collapse through time evolution. For two-level systems, we put forward the phenomenon of chiral state conversion as a mechanism effectively eliminating superpositions.
  arXiv  Detail & Related papers  (2024-08-08T17:59:10Z)
• Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
  We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state.
  arXiv  Detail & Related papers  (2023-05-06T18:09:17Z)
• Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure [49.1574468325115]
  We study the entanglement of a single particle under continuous measurements. We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
  arXiv  Detail & Related papers  (2023-04-06T09:45:11Z)
• Stochastic approach to evolution of a quantum system interacting with a wave packet in squeezed number state [0.0]
  We determine filtering and master equations for a quantum system interacting with wave packet of light in a continuous-mode squeezed number state. We formulate the problem of conditional evolution of a quantum system making use of model of repeated interactions and measurements.
  arXiv  Detail & Related papers  (2023-03-21T19:42:15Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Coalescence of non-Markovian dissipation, quantum Zeno effect and non-Hermitian physics, in a simple realistic quantum system [0.0]
  We develop a theoretical framework in terms of the time-dependent Schrodinger equation of motion. The link between the peaked structure of the effective decay rate of the qubit that interacts indirectly with the environment, and the onset of the quantum Zeno effect is discussed in great detail. Our treatment and results have revealed an intricate interplay between non-Markovian dynamics, quantum Zeno effect and non-Hermitian physics.
  arXiv  Detail & Related papers  (2022-06-28T09:28:02Z)
• Measurement induced quantum walks [0.0]
  We investigate a quantum walk on a graph with classical and quantum mechanical properties. For a quantum walk on a line we show that in our system the first detection probability decays classically like $(texttime)-3/2$.
  arXiv  Detail & Related papers  (2021-08-30T08:11:24Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)
• Measurement-induced quantum criticality under continuous monitoring [0.0]
  We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength. We propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations.
  arXiv  Detail & Related papers  (2020-04-24T19:35:28Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.