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Optical and Quantum Sensing and Precision Metrology II

Reservoir-engineered spin squeezing: macroscopic even-odd effects and hybrid-systems implementations

Martin Koppenhöfer, Peter Groszkowski, Hoi-Kwan Lau, Aashish A. Clerk

Published Mar 9, 2022• 0 citations
Publisher

Abstract

We revisit the dissipative approach to producing and stabilizing spin-squeezed states of an ensemble of N two-level systems, providing a detailed analysis of two surprising yet generic features of such protocols. The first is a macroscopic sensitivity of the steady state to whether N is even or odd. We discuss how this effect can be avoided (if the goal is parity-insensitive squeezing), or could be exploited as a new kind of sensing modality to detect the addition or removal of a single spin. The second effect is an anomalous emergent long timescale and a "prethermalized" regime that occurs for even weak single-spin dephasing. We also discuss a general hybrid-systems approach for implementing dissipative spin squeezing that does not require squeezed input light or complex multi-level atoms, but instead makes use of bosonic reservoir-engineering ideas. Our protocol is compatible with a variety of platforms, including trapped ions, NV defect spins coupled to diamond optomechanical crystals, and spin ensembles coupled to superconducting microwave circuits.

DOI
10.1117/12.2616978

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We revisit the dissipative approach to producing and stabilizing spin-squeezed states of an ensemble of N two-level systems, providing a detailed analysis of two surprising yet generic features of such protocols. The first is a macroscopic sensitivity of the steady state to whether N is even or odd. We discuss how this effect can be avoided (if the goal is parity-insensitive squeezing), or could be exploited as a new kind of sensing modality to detect the addition or removal of a single spin. The second effect is an anomalous emergent long timescale and a "prethermalized" regime that occurs for even weak single-spin dephasing. We also discuss a general hybrid-systems approach for implementing dissipative spin squeezing that does not require squeezed input light or complex multi-level atoms, but instead makes use of bosonic reservoir-engineering ideas. Our protocol is compatible with a variety of platforms, including trapped ions, NV defect spins coupled to diamond optomechanical crystals, and spin ensembles coupled to superconducting microwave circuits.
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Abstract Spin squeezing, a form of many-body entanglement, is a crucial resource in quantum metrology and information processing. While experimentally viable protocols for generating stable spin squeezing have been proposed in quantum optics setups, there is growing interest in quantum hybrid solid-state systems as alternative platforms for both engineering and exploring many-body quantum phenomena. In this work, we propose a scheme to generate long-lived spin squeezing in an ensemble of solid-state qubits interacting with electromagnetic noise emitted by a squeezed solid-state bath. We identify the conditions under which quantum correlations within the bath can be transferred to the qubit array, driving it into an entangled state independently of its initial configuration. To assess the experimental feasibility of our approach, we analyze the dynamics of an array of solid-state spin defects coupled to a common ferromagnetic bath, which is driven into a non-equilibrium squeezed state through its interaction with a surface acoustic wave mode. Our results demonstrate that the ensemble can exhibit steady-state spin squeezing under suitable conditions, opening new pathways for the generation of robust many-body entanglement in solid-state spin ensembles.
We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, NNN two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which, in the squeezed representation, effectively transforms the collective spin operators into a Bogoliubov form. Under large detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling a two-axis twisting squeezing protocol through appropriate parameter tuning. Both theoretical analysis and numerical simulations show that in the presence of dephasing and phonon dissipation, the maximum squeezing degree asymptotically converges to a constant as NNN increases, which implies the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract a scaling relation of the optimal squeezing which surpasses existing schemes in the literature. Moreover, the optimization also leads to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.
We discuss how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes. The scheme does not rely on any explicit measurement or feedback, nor does it simply involve a modulation of an optical spring constant. Instead, it uses a dissipative mechanism with the driven cavity acting as an engineered reservoir. It can equivalently be viewed as a coherent feedback process, obtained by minimally perturbing the quantum nondemolition measurement of a single mechanical quadrature. This shows that in general the concepts of coherent feedback schemes and reservoir engineering are closely related. We analyze how to optimize the scheme, how the squeezing scales with system parameters, and how it may be directly detected from the cavity output. Our scheme is extremely general, and could also be implemented with, e.g., superconducting circuits.
The hybridization of distinct quantum systems has now reached the stage when we can actually engineer the properties of the composite system to be better than the individual parts. One natural application of hybridization is the generation of non-classical states, which are extremely important in emerging quantum technologies such as quantum metrology and sensing. In this presentation we consider the generation of spin squeezed states in a hybrid system composed of a superconducting circuit coupled to a spin ensemble. We show that spin squeezing can be generated by two different mechanisms: one-axis twisting and driven collective relaxation.