A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose–Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom–atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.
A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose–Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom–atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.
Recently, a method has been proposed to detect the rotation of a ring Bose-Einstein condensate, , in real-time, and with minimal destruction by using a cavity driven with optical fields carrying orbital angular momentum []. This method is sensitive to the magnitude of the condensate winding number but not its sign. In the present work, we consider simulations of the rotation of the angular lattice formed by the optical fields and show that the resulting cavity transmission spectra are sensitive to the sign of the condensate winding number. We demonstrate the minimally destructive technique on persistent current rotational eigenstates, counter-rotating superpositions, and a soliton singly or in collision with a second soliton. Conversely, we also investigate the sensitivity of the ring condensate, given knowledge of its winding number, to the rotation of the optical lattice. This characterizes the effectiveness of the optomechanical configuration as a laboratory rotation sensor. Our results are important to studies of rotating ring condensates used in atomtronics, superfluid hydrodynamics, simulation of topological defects and cosmological theories, interferometry using matter-wave solitons, and optomechanical sensing. Published by the American Physical Society 2024
Atomic superfluids formed using Bose-Einstein condensates (BECs) in a ring trap are currently investigated in the context of superfluid hydrodynamics, quantum sensing, and matter-wave interferometry. The characterization of the rotational properties of such superfluids is important, but can presently only be performed by using optical absorption imaging, which completely destroys the condensate. Recent studies have proposed coupling the ring BEC to optical cavity modes carrying orbital angular momentum to make minimally destructive measurements of the condensate rotation. The sensitivity of these proposals, however, is bounded below by the standard quantum limit set by the combination of laser shot noise and radiation pressure noise. In this work we provide a theoretical framework that exploits the fact that the interaction between the scattered modes of the condensate and the light reduces to effective optomechanical equations of motion. We present a detailed theoretical analysis to demonstrate that the use of squeezed light and backaction evasion techniques allows the angular momentum of the condensate to be sensed with noise well below the standard quantum limit. Our proposal is relevant to atomtronics, quantum sensing, and quantum information.
Recent great progress in studying theoretical and especially experimental properties of Bose Einstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in two dimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for two body interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.
Recent great progress in studying theoretical and especially experimental properties of BoseEinstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in twodimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for twobody interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.
We theoretically investigate an annularly confined Bose-Einstein Condensate (BEC) coupled to a four-mirror ring cavity supporting traveling-wave optical modes. Under symmetric driving by counter-propagating Laguerre-Gaussian beams carrying equal and opposite orbital angular momenta, the system realizes supersolid phases coexisting with persistent superfluid circulation. Specifically, we obtain a supersolid state if we start with a BEC of winding number Lp as well as supersolid packets with coherent superpositions of two different BEC Lp values. Under asymmetric pumping, realized with Laguerre-Gaussian beams of different orbital angular momenta, chiral symmetry is broken in the system, resulting in asymmetric cavity field amplitudes, directional density modulations, and tunable rotational dynamics of the resulting supersolid lattice. This leads to rotating supersolid density structures for a single winding-number state, and rotating wave packets for an initial superposition of rotational eigenstates. Finally, we probe the presence of Goldstone and Higgs modes which can be observed using minimally destructive measurements of the cavity output spectrum. Our mean-field theory reveals interference-driven rotation without physical stirring, and distinguishes our work from prior static cavity supersolids. Our results establish the ring cavity annular BEC as a versatile platform for generating chiral quantum matter, implementing rotation-sensing devices and generating atomtronic circuits with supersolids.
We theoretically analyze the operating principles of a proposed matter-wave Sagnac interferometer utilizing Bose-Einstein-condensate (BEC) phonon modes as an interference medium. Previous work found that the orbital angular momentum phonon modes of a ring-trapped BEC are split in frequency by rotations, leading to a measurable rotation signal. We develop an alternate description in which an imbalance in the counterpropagating modes' amplitudes (populations) is induced by the rotation of the system during condensation. This description gives analytic forms for the interferometic phase shift in one dimension and is readily generalized to include mean-field interactions. To validate our findings, we simulate a ring-trapped BEC Sagnac interferometer in one dimension and demonstrate that measurement of an unknown rotation rate can be performed using a modified analysis. Our simulation data show strong agreement with our analytic results, and we further employ simulations to explore and clarify the role of superfluidity in this matter-wave Sagnac interferometer.