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arXiv:2007.13805 · Physical Chemistry Chemical Physics

Spin-momentum entanglement in a Bose–Einstein condensate

Sumit Suresh Kale, Yijue Ding, Yong P. Chen, Břetislav Friedrich, Sabre Kais

Published Jan 1, 2020• 6 citations
arXivHTMLPDF

Abstract

Entanglement is at the core of quantum information processing and may prove essential for quantum speed-up. Inspired by both theoretical and experimental studies of spin-momentum coupling in systems of ultra-cold atoms, we investigate the entanglement between the spin and momentum degrees of freedom of an optically trapped BEC of 87Rb atoms. We consider entanglement that arises due to the coupling of these degrees of freedom induced by Raman and radio-frequency fields and examine its dependence on the coupling parameters by evaluating von Neumann entropy as well as concurrence as measures of the entanglement attained. Our calculations reveal that under proper experimental conditions significant spin-momentum entanglement can be obtained, with von Neumann entropy of 80% of the maximum attainable value. Our analysis sheds some light on the prospects of using BECs for quantum information applications.

DOI
10.1039/d0cp03945d

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Entanglement is at the core of quantum information processing and may prove essential for quantum speed-up. Inspired by both theoretical and experimental studies of spin-momentum coupling in systems of ultra-cold atoms, we investigate the entanglement between the spin and momentum degrees of freedom of an optically trapped BEC of 87Rb atoms. We consider entanglement that arises due to the coupling of these degrees of freedom induced by Raman and radio-frequency fields and examine its dependence on the coupling parameters by evaluating von Neumann entropy as well as concurrence as measures of the entanglement attained. Our calculations reveal that under proper experimental conditions significant spin-momentum entanglement can be obtained, with von Neumann entropy of 80% of the maximum attainable value. Our analysis sheds some light on the prospects of using BECs for quantum information applications.
Abstract We show that the general quantum state of synthetically spin–orbit coupled ultra cold bosonic atoms, whose condensate was experimentally created recently by Lin et al (2011 Nature 471 , 83), shows entanglement between motional degrees of freedom (momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provide a unique opportunity to verify fundamental principles like quantum contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such an atom-laser system and how this influences quantities like entanglement entropy, the violation of Bell-like inequality, etc. We also discuss the implications of our result in testing quantum contextuality and Bell’s Inequality violation by macroscopic quantum object like Bose–Einstein condensate of ultra cold atoms.
We demonstrate coupling between the atomic spin- and orbital-angular momentum (OAM) of the atom's center-of-mass motion in a Bose-Einstein condensate (BEC). The coupling is induced by Raman-dressing lasers with a Laguerre-Gaussian beam and creates coreless vortices in an F=1 ^{87}Rb spinor BEC. We observe correlations between spin and OAM in the dressed state and characterize the spin texture; the result is in good agreement with the theory. In the presence of the Raman field, our dressed state is stable for 0.1 s or longer, and it decays due to collision-induced relaxation. As we turn off the Raman beams, the vortex cores in the bare spin |m_{F}=1⟩ and |-1⟩ split. These spin-OAM coupled systems with the Raman-dressing approach have great potential for exploring new topological textures and quantum states.
Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers open up unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise is large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers promise unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
The predictions of quantum mechanics often differ from our everyday experiences. In the classical case, the state of a system can be predicted precisely, assuming the exact knowledge of all parameters. This is not possible in quantum mechanics. For example, the spin of one particle can be simultaneously in two different states, until a measurement defines the actual state. If multiple particles are in such superposition states, their spins can be coupled with each other such that the measurement of one particle changes the physical state of the other particles. This coupling effect is a fundamental part of quantum mechanics and is called entanglement. It is a central requirement for applications in the fields of quantum communication, quantum cryptography and quantum computing. One possibility to create entanglement are spin-changing collisions in a spinor Bose-Einstein condensate. These collisions are described by a nonlinear process, which creates non-classical correlations between all atoms of the Bose-Einstein condensate. Within this thesis, 87Rb spinor Bose-Einstein condensates are used to demonstrate Einstein-Podolsky-Rosen entanglement by the generation and analysis of a two-mode entangled state in spin space [A1]. These states are applied in an interferometric measurement with a resolution of 2.05+0.34 -0.37 dB beyond the standard quantum limit [A2]. Depending on the dynamics, the process can also be analogous to the dynamical Casimir effect [A3]. The entanglement between the particles in these publications is strongly connected with their indistinguishability. It is thus possible to make the particles distinguishable again and recover the entanglement between the now separated particles? This question is approached by cutting an entangled state of indistinguishable particles into two spatially separated atomic modes - creating a two-mode entangled state in real space. As shown in Ref. [A4], the entanglement between the two separated clouds of a Bose-Einstein condensate can be measured directly. In the future, the created state can be employed for a test of quantum nonlocality.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.