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Journal of Physics B Atomic Molecular and Optical Physics

Seeded spin-mixing interferometry with long-time evolution in microwave-dressed sodium spinor Bose-Einstein condensates

Shan Zhong, Hio Giap Ooi, Sankalp Prajapati, Qimin Zhang, Arne Schwettmann

Published Mar 10, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/acc36f

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Communications in Theoretical Physics•Dec 20, 2021•1 citation
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 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 $t\ensuremath{\gg}h/c$, 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 ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states.
The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F=1F=1F=1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of $|F=1,m=\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ atoms. We simulate the effect of single- and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single- and double-sided seeding we find there exists an optimal phase shift that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na^{23}\mathrm{Na}23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier and demonstrate sensitivity to initial population fractions as small as 0.1%.
Most interferometers operate with photons or dilute, noncondensed cold atom clouds in which collisions are strongly suppressed. Spinor Bose-Einstein condensates (BECs) provide an alternative route toward realizing three-mode interferometers; in this realization, spin-changing collisions provide a resource that generates mode entanglement. Working in the regime where the pump mode, i.e., the m=0m=0m=0 hyperfine state, has a much larger population than the side or probe modes ($m=\ifmmode\pm\else\textpm\fi{}1$ hyperfine states), f=1f=1f=1 spinor BECs approximate SU(1,1) interferometers. We derive analytical expressions within the undepleted pump approximation for the phase sensitivity of such an SU(1,1) interferometer for two classes of initial states: pure Fock states and coherent spin states. The interferometer performance is analyzed for initial states without seeding, with single-sided seeding, and with double-sided seeding. The validity regime of the undepleted pump approximation is assessed by performing quantum calculations for the full spin Hamiltonian. Our analytical results and the associated dynamics are expected to guide experiments as well as numerical studies that explore regimes where the undepleted pump approximation makes quantitatively or qualitatively incorrect predictions.
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.
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 simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose–Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spin-nematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.