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arXiv:2201.03918 · Physical Review Letters

Quantum Nondemolition Measurements of Moving Target States

Anton L. Andersen, Klaus Mølmer

Published Sep 14, 2022• 5 citations
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Abstract

We present a protocol for probing the state of a quantum system by its resonant coupling and entanglement with a meter system. By continuous measurement of a time evolving meter observable, we infer the evolution of the entangled systems and, ultimately, the state and dynamics of the system of interest. The photon number in a cavity field is thus resolved by simulated monitoring of the Rabi oscillations of a resonantly coupled two-level system, and we propose to regard this as a practical extension of quantum nondemolition measurements with applications in quantum metrology and quantum computing.

DOI
10.1103/physrevlett.129.120402

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We present a protocol for probing the state of a quantum system by its resonant coupling and entanglement with a meter system. By continuous measurement of a time evolving meter observable, we infer the evolution of the entangled systems and, ultimately, the state and dynamics of the system of interest. The photon number in a cavity field is thus resolved by simulated monitoring of the Rabi oscillations of a resonantly coupled two-level system, and we propose to regard this as a practical extension of quantum nondemolition measurements with applications in quantum metrology and quantum computing.
A quantum system can be monitored through repeated interactions with meter systems. The state of the system at time ttt, represented by the density matrix $\ensuremath{\rho}(t)$, then becomes conditioned on the information obtained by the meters until that time. More insight in the state of the system at any time ttt is provided, however, by taking into account the full detection of all meters interacting with the system both in the past and in the future of ttt. We present experiments that use near-resonant atomic probes to monitor the evolution of the quantized field in a cavity. The application of the forward-backward smoothing method to this quantum problem, justified by the past quantum state formalism [S. Gammelmark et al., Phys. Rev. Lett. 111, 160401 (2013)], allows us to resolve a posteriori dynamics, which is not reflected by the usual quantum state $\ensuremath{\rho}(t)$.
A specific measurement model based on quantum nondemolition monitoring of oscillator quanta is used to illustrate the essential elements of the quantum theory of measurement, viz., state reduction and existence of a ``pointer basis,'' recently discussed by Zurek. The form of the interaction between the meter and its environment determines the system observable recorded by the meter. In our model this quantity is the square of the oscillator's quanta. The corresponding pointer basis states are the meter coherent states. The more accurate the measurement the more excited (and classical) these states become. We show explicitly that the state reduction of the system during measurement is due to nonunitary evolution resulting from the meter-environment coupling. A particular realization of the environment as a photoelectron counter is discussed.
The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling, fulfilling quantum nondemolition criteria. Two schemes of measurements are examined. The first one consists of measuring the atomic electric dipole, which indirectly allows one to infer the photon distribution inside the cavity. The second one schematizes a measurement of photon momentum, which permits one to describe the atomic level distribution. Decoherence of the corresponding reduced density matrices is studied in detail for both cases, and its relationship to recent experiments is finally discussed.
We discuss monitoring the time evolution of an analog quantum simulator via a quantum nondemolition (QND) coupling to an auxiliary "clock" qubit.The QND variable of interest is the "energy" of the quantum many-body system, represented by the Hamiltonian of the quantum simulator.We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser-dressing schemes for a broad class of spin models.As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to identify signatures of ergodic versus nonergodic dynamics, which we illustrate for disordered one-dimensional Heisenberg and Floquet spin models on Rydberg platforms.Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator.
A continuous quantum-nondemolition measurement scheme that is based on intensity dependent atomic scattering in three-state systems is analyzed. The proposed scheme measures the number of photons in an optical cavity mode by observing the scattering rate of the atomic medium. The time evolution of the coupled atom-field system is analyzed using the Monte Carlo wave-function approach. The wave-function collapse occurs continuously as a result of the presence or absence of scattering events at each time instant. It is shown that the measurement is logically reversible and the information contained in the premeasurement wave function is preserved during the measurement interaction.