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. This effect allows one to have strong spin squeezing over a long transient time even though the level of spin squeezing in the steady state is very small. 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.
Highlights
Among the most sought-after states in quantum metrology are spin-squeezed states, highly entangled states of spin-1=2 ensembles that enable parameter sensing with a sensitivity better than the standard quantum limit, even reaching fundamental Heisenberg-limit scaling [1,2]
The second effect is an anomalous emergent long timescale and a “prethermalized” regime that occurs for even weak single-spin dephasing. This effect allows one to have strong spin squeezing over a long transient time even though the level of spin squeezing in the steady state is very small
Perhaps most striking is the extreme sensitivity of dissipative spin squeezing to the parity of the total number of spins N: The steady state is macroscopically different for N spins versus N þ 1 spins
Summary
Among the most sought-after states in quantum metrology are spin-squeezed states, highly entangled states of spin-1=2 ensembles that enable parameter sensing with a sensitivity better than the standard quantum limit, even reaching fundamental Heisenberg-limit scaling [1,2]. We consider coupling the cavity to an auxiliary lossy degree of freedom (two-level system or bosonic mode), which is driven simultaneously with imbalanced red-detuned and blue-detuned sideband drives Such schemes produce an effective squeezed dissipator for the cavity and have been experimentally implemented in a wide variety of platforms, including optomechanics [15], trapped ions [16], and superconducting circuits [20]. Perhaps most striking is the extreme sensitivity of dissipative spin squeezing to the parity of the total number of spins N: The steady state is macroscopically different for N spins versus N þ 1 spins While this effect was implicitly contained in the results of Agarwal and Puri [21,22] (see Sec. VIII for a detailed discussion of the relation to previous works), we provide here a fully qualitative and quantitative analysis.
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