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arXiv:1909.03361 · Physical Review A

Quantum interferometry with microwave-dressed F=1 spinor Bose-Einstein condensates: Role of initial states and long-time evolution

Qimin Zhang, Arne Schwettmann

Published Dec 26, 2019• 7 citations
arXivHTMLPDF

Abstract

We numerically investigate atomic interferometry based on spin-exchange collisions in $F=1$ spinor Bose-Einstein condensates in the regime of long evolution times $t\ensuremath{\gg}h/c$, where $c$ is the spin-dependent interaction energy. We show that the sensitivity of spin-mixing interferometry can be enhanced by using classically seeded initial states with a small population prepared in the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states.

DOI
10.1103/physreva.100.063637

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We numerically investigate atomic interferometry based on spin-exchange collisions in F=1F=1F=1 spinor Bose-Einstein condensates in the regime of long evolution times t\ensuremath≫h/ct\ensuremath{\gg}h/ct\ensuremath≫h/c, where ccc is the spin-dependent interaction energy. We show that the sensitivity of spin-mixing interferometry can be enhanced by using classically seeded initial states with a small population prepared in the mF=\ifmmode±\else\textpm\fi1{m}_{F}=\ifmmode\pm\else\textpm\fi{}1mF​=\ifmmode±\else\textpm\fi1 states.
Abstract We experimentally demonstrate a new type of spin-mixing interferometry in sodium Bose–Einstein condensates (BECs) based on seeded initial states. Seeding is useful because it speeds up the generation of entangled pairs, allowing many collisions to take place quickly, creating large populations in the arms of the interferometer. The entangled probe states of our interferometer are generated via spin-exchange collisions in F = 1 spinor BECs, where pairs of atoms with the magnetic quantum number m F = 0 collide and change into pairs with m F = ± 1 . Our results show that our seeded spin-mixing interferometer beats the standard quantum limit (SQL) with a metrological gain of 3.69 dB with spin-mixing time t = 10 ms in the case of single-sided seeding, and 3.33 dB with spin-mixing time t = 8 ms in the case of double sided seeding. The mechanism for beating the SQL is two-mode spin squeezing generated via spin-exchange collisions. Our results on spin-mixing interferometry with seeded states are useful for future quantum technologies such as quantum-enhanced microwave sensors, and quantum parametric amplifiers based on spin-mixing.
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.
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We theoretically investigate how entangled atomic states generated via spin-changing collisions in a spinor Bose-Einstein condensate can be designed and controllably prepared for atom interferometry that is robust against common technical issues, such as limited detector resolution. We use analytic and numerical treatments of the spin-changing collision process to demonstrate that triggering the entangling collisions with a small classical seed rather than vacuum fluctuations leads to a more robust and superior sensitivity when technical noise is accounted for, despite the generated atomic state ideally featuring less metrologically useful entanglement. Our results are relevant for understanding how entangled atomic states are best designed and generated for use in quantum-enhanced matter-wave interferometry.
We study the time-evolution of an optically trapped spinor Bose-Einstein condensate under the influence of a dominating magnetic bias field in the z-direction, and a perpendicular smaller field that couples the spinor states. We show that if the bias field depends quadratically on time, the relative phases of the spinor components affect the populations of the final state. This allows one to measure the differences in the time-evolution of the relative phases, thereby realizing a multi-arm interferometer in a spinor Bose-Einstein condensate.