Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

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 quantumenhanced 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.Nonlinear dynamics is the basis of generating nonclassical states of many particles. These entangled states are capable of improving a large variety of operations, e.g., computational tasks [1], communication and measurements [2]. Unlocking their full potential for quantum technologies requires both the generation and detection at the fundamental quantum limit. The generation of such highly entangled states with many particles has witnessed tremendous advances [3,4]. However, to fully exploit this quantum resource, the complete correlations on the single particle level need to be accessed, which still limits current experiments.To address this challenge, nonlinear readout schemes have been proposed [5][6][7][8]. Most of these employ a time inversion sequence. For this the nonlinear evolution that is used to produce the entangled state is inverted and reapplied for readout. If the state remains unperturbed, the second period of nonlinear evolution counteracts the first. This time-reversed readout disentangles the probe state such that the known separable initial state is recovered. This reversibility is nonperfect if the state is changed in between, similar to an incomplete Loschmidt-Echo [9]. By this sensitive mechanism, minute state perturbations are mapped onto readily discernable quantities.Experimentally, we use spin-changing collisions [10] in a mesoscopic spinor Bose-Einstein condensate. This nonlinear mechanism is the atomic analogue of parametric amplification, which is the textbook example of entangled state generation in quantum optics. At the same time, both the sign and the strength of the nonlinear coupling are experimentally adjustable, which makes this system ideally suited for realizing time reversal readout schemes.Spin exchange is performed in an effective three-level system within the spin F = 2 manifold of 87 Rb. For this the external degrees of freedom are frozen out such that dynamics is restricted to the spin degree of freedom. We start with a pure |F = 2, m F = 0 condensate (pump mode). Population in any m F = 0 state is carefully cleaned. During spin mixing atoms of the pump mode are coherently and pairwise scattered into the signal |↑ ≡ |2, 1 and idler |↓ ≡ |2, −1 mode, which we refer to as side modes (see Fig. 1). For small p...

Inflationary preheating dynamics with two-species condensates

“…Experimentally, we have in mind the twin-atom beam experiments of the Schmiedmayer laboratories [9], and the spin-changing collision dynamics arising in bosonic spin-one systems as employed by the Oberthaler group [10]. We identify the relevant dynamical processes of the cold-atom system and describe * zache@thphys.uni-heidelberg.de them using quantum-statistical field theory.…”

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

“…The protocols demonstrated here are widely applicable and could be implemented in a variety of other platforms with reversible dynamics, such as linear ion chains [20,24], ultracold atomic gases [4,5,25], cold atoms in optical cavities [26][27][28], Rydberg-dressed atoms [29], superconducting qubits [30], and NMR systems [22].…”

“…These generalizations will allow us to explore the dynamics of OTOCs and characterize scrambling in unexplored regimes and under conditions where fast scrambling can occur. Furthermore, the ability to time-reverse the dynamics will allow enhanced phase estimation without single particle detection resolution [5,29,37], investigations of quantum phase transitions [38], criticality [39], thermalization in nearly closed quantum systems [13,40] exploration of the quantum-classical boundary [41], e.g., observation of the violation of Leggett-Garg inequalities [42].…”

“…Ludwig Boltzmann responded by formulating the probabilistic definition of entropy, one of the cornerstones of statistical mechanics, and, now a fundamental concept in quantum information. Since the days of Boltzmann and Loschmidt, the notion of time-reversal has moved from the arena of thought experiments into the laboratory, with time-reversal of non-interacting quantum systems in the form of Hahn spin echoes [2] forming an essential part of nuclear magnetic resonance (NMR) [3] and magnetic resonance imaging.Recently, the experimental implementation of manybody time-reversal protocols [4,5] in atomic quantum systems have attracted attention [6][7][8][9] for their potential to quantify the flow of quantum information in time and set bounds on thermalization times [10][11][12][13], which might also enable experimental tests of the holographic duality between quantum and gravitational systems [6,[14][15][16][17]. The key quantities sought after are special types of outof-time-order correlation (OTOC) functions,…”

“…Recently, the experimental implementation of manybody time-reversal protocols [4,5] in atomic quantum systems have attracted attention [6][7][8][9] for their potential to quantify the flow of quantum information in time and set bounds on thermalization times [10][11][12][13], which might also enable experimental tests of the holographic duality between quantum and gravitational systems [6,[14][15][16][17]. The key quantities sought after are special types of outof-time-order correlation (OTOC) functions,…”