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arXiv:1602.07505 · Physical Review Letters

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

Daniel Linnemann, Helmut Strobel, Wolfgang Muessel, J. Schulz, Robert J. Lewis-Swan, Karen V. Kheruntsyan, Markus K. Oberthaler

Published Jun 28, 2016• 220 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

DOI
10.1103/physrevlett.117.013001

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We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.
Discrimination of entangled states is an important element of quantum-enhanced metrology. This typically requires low-noise detection technology. Such a challenge can be circumvented by introducing nonlinear readout process. Traditionally, this is realized by reversing the very dynamics that generates the entangled state, which requires a full control over the system evolution. In this Letter, we present nonlinear readout of highly entangled states by employing reinforcement learning to manipulate the spin-mixing dynamics in a spin-1 atomic condensate. The reinforcement learning found results in driving the system toward an unstable fixed point, whereby the (to be sensed) phase perturbation is amplified by the subsequent spin-mixing dynamics. Working with a condensate of 10 900 ^{87}Rb atoms, we achieve a metrological gain of 6.97_{-1.38}^{+1.30} dB beyond the classical precision limit. Our work will open up new possibilities in unlocking the full potential of entanglement caused quantum enhancement in experiments.
Quantum-enhanced metrology relies on entanglement to achieve sensitivities beyond the standard quantum limit. While remarkable progress has been made in generating highly entangled many-body states, extracting their metrological advantage remains a central challenge because the encoded information is often inaccessible to realistic measurements. A key development of the past decade has been the realization that many-body interactions can play a dual role: they can be used not only to generate entanglement, but also to decode it. This idea underlies interaction-based readout and time-reversal protocols, in which controlled non-linear dynamics transform weakly encoded signals into experimentally accessible observables. Cavity quantum electrodynamics (QED) provides a particularly powerful setting for these approaches because it combines collective enhancement, tunable interactions, and controllable reversibility within a single platform. In this review, we discuss the emergence of time-reversal protocols in cavity QED, from their conceptual roots in Loschmidt echoes to modern implementations of signal amplification through a time-reversed interaction (SATIN), scrambling-enhanced metrology, and more general interaction-based readout schemes. We examine the physical mechanisms that enable reversible many-body dynamics, review key experimental demonstrations, and discuss future directions involving complex entangled states, nonlinear decoding, and emerging quantum platforms. Together, these developments suggest that the ability to decode quantum information may become as important as the ability to generate it, establishing reversible many-body dynamics as a central resource for quantum-enhanced sensing.
Abstract Active interferometers use amplifying elements for beam splitting and recombination. We experimentally implement such a device by using spin exchange in a Bose–Einstein condensate. The two interferometry modes are initially empty spin states that get spontaneously populated in the process of parametric amplification. This nonlinear mechanism scatters atoms into both modes in a pairwise fashion and generates a non-classical state. Finally, a matched second period of spin exchange is performed that nonlinearly amplifies the output signal and maps the phase onto readily detectable first moments. Depending on the accumulated phase this nonlinear readout can reverse the initial dynamics and deamplify the entangled state back to empty spin states. This sequence is described in the framework of SU(1,1) mode transformations and compared to the SU(2) angular momentum description of passive interferometers.
Abstract We propose a scheme that a dynamically evolving atom-molecule condensate maps onto an SU(1, 1) interferometer, which includes a nonlinear medium (nonlinear phase encoding). We give an analytical result of the phase uncertainty from the error propagation by measuring the particle number at the output and demonstrate the optimal quantum metrology, which is obtained with a time-reversal protocol. We show the phase sensitivity of the nonlinear medium with time-reversal protocol scales as 1/(2.1 N 2 ), which overcome the conventional sensitivity limit of 1/ N . Finally, the effect of the poor particle resolution detection on the phase sensitivity is discussed.
We propose and analyze a quantum interferometry scheme based on a Raman-dressed Bose gas with spin-orbit coupling. In this system, the atom-light coupling mixes spin and momentum degrees of freedom, giving rise, in the low-energy regime, to an effective spinor condensate whose spin-mixing interaction can be tuned independently of the atomic density. This controllability enables a separation between state preparation and phase imprinting, and provides a natural route to echo-type protocols based on effective time reversal. Within this framework, critical regimes of the effective spinor Hamiltonian can be used to generate entanglement and enhance interferometric sensitivity beyond the standard quantum limit. In addition, the spin-momentum locking of the dressed modes gives access to spatial density modulations that provide an alternative readout of the interferometric phase. In particular, phase information can be extracted from the displacement of spin-orbit-induced density stripes even when conventional spin observables are insensitive within the effective spinor description. Our results identify Raman-dressed spinor gases as a flexible platform for nonlinear atomic interferometry, combining controllable spin-mixing dynamics with spatially resolved phase readout.
Atom interferometer has been proven to be a powerful tool for precision metrology. Here we propose a cavity-aided nonlinear atom interferometer, based on the quasi-periodic spin mixing dynamics of an atomic spin-1 Bose–Einstein condensate trapped in an optical cavity. We unravel that the phase sensitivity can be greatly enhanced with the cavity-mediated nonlinear interaction. The influence of encoding phase, splitting time and recombining time on phase sensitivity are carefully studied. In addition, we demonstrate a dynamical phase transition in the system. Around the criticality, a small cavity light field variation can arouse a strong response of the atomic condensate, which can serve as a new resource for enhanced sensing. This work provides a robust protocol for cavity-enhanced metrology.