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arXiv:2011.13190

Bose-Einstein condensate soliton qubit states for metrological applications

The Vinh Ngo, Dmitriy V. Tsarev, Ray‐Kuang Lee, A. P. Alodjants

Published Nov 26, 2020• 0 citations
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Abstract

By utilizing Bose-Einstein condensate solitons, optically manipulated and trapped in a double-well potential, coupled through nonlinear Josephson effect, we propose novel quantum metrology applications with two soliton qubit states. In addition to steady-state solutions in different scenarios, phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes. Schrödinger-cat states, maximally path-entangled ($N00N$) states, and macroscopic soliton qubits are predicted and exploited for the distinguishability of obtained macroscopic states in the framework of binary (non-orthogonal) state discrimination problem. For arbitrary phase estimation in the framework of linear quantum metrology approach, these macroscopic soliton states are revealed to have a scaling up to the Heisenberg limit (HL). The examples are illustrated for HL estimation of angular frequency between the ground and first excited macroscopic states of the condensate, which opens new perspectives for current frequency standards technologies.

DOI
10.48550/arxiv.2011.13190

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Abstract We propose a novel platform for quantum metrology based on qubit states of two Bose-Einstein condensate solitons, optically manipulated, trapped in a double-well potential, and coupled through nonlinear Josephson effect. We describe steady-state solutions in different scenarios and perform a phase space analysis in the terms of population imbalance - phase difference variables to demonstrate macroscopic quantum self-trapping regimes. Schrödinger-cat states, maximally path-entangled (N00N) states, and macroscopic soliton qubits are predicted and exploited to distinguish the obtained macroscopic states in the framework of binary (non-orthogonal) state discrimination problem. For arbitrary phase estimation in the framework of linear quantum metrology approach, these macroscopic soliton states are revealed to have a scaling up to the Heisenberg limit (HL). The examples illustrate the HL estimation of angular frequency between the ground and first excited macroscopic states of the condensate, which opens new perspectives for current frequency standard technologies.
We propose a novel platform for quantum metrology based on qubit states of two Bose-Einstein condensate solitons, optically manipulated, trapped in a double-well potential, and coupled through nonlinear Josephson effect. We describe steady-state solutions in different scenarios and perform a phase space analysis in the terms of population imbalance-phase difference variables to demonstrate macroscopic quantum self-trapping regimes. Schrödinger-cat states, maximally path-entangled (N00N) states, and macroscopic soliton qubits are predicted and exploited to distinguish the obtained macroscopic states in the framework of binary (non-orthogonal) state discrimination problem. For an arbitrary frequency estimation we have revealed these macroscopic soliton states have a scaling up to the Heisenberg and super-Heisenberg (SH) limits within linear and nonlinear metrology procedures, respectively. The examples and numerical evaluations illustrate experimental feasibility of estimation with SH accuracy of angular frequency between the ground and first excited macroscopic states of the condensate in the presence of moderate losses, which opens new perspectives for current frequency standard technologies.
Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition state and maximally path entangled N00N-state. We examine these macroscopic states by Mach-Zehnder interferometer in the context of parity measurements, which has been done to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio of two-body scattering length to intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.
The estimation of some parameters with super-Heisenberg (SH) sensitivity, i.e. beyond Heisenberg limit, is one of the principal problems for current quantum metrology. We propose to use Bose–Einstein condensate quantum bright solitons for this purpose. We have shown that solitons, as quantum nonlinear structured field objects, allow SH phase estimation even with coherent probes in the framework of a nonlinear metrology approach. To achieve ultimate scaling in nonlinear phase estimation, which is 1/ N 3 , we examine soliton phase shift occurring due to interaction of weakly coupled 1D solitons. We have shown that steady states of coupled solitons can be used for the formation of maximally path-entangled N 00 N -state providing minimal propagation error of solitons’ relative distance, momentum, and atom–atom scattering length parameter.
By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition states and maximally path entangled N00N-states. We examine Mach- Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.
We propose and numerically validate a scheme for the realization of Schrödinger cat-like states in a two-component Bose-Einstein condensate, emphasizing their twinning across components under tunable intra- and inter-species interactions within the miscibility regime. Wigner phase-space analysis reveals sub-Planck-scale interference fringes, confirming the nonclassical character of the states and their potential utility in quantum-enhanced metrology. The dynamical response of the system to a weak linear gravitational-like perturbation further demonstrates cooperative enhancement: while the directly perturbed component retains its cat-like features, the coupled partner exhibits a pronounced population imbalance and a distinct phase-space rotation, providing a sensitive detection channel absent in single-component condensates. These results establish binary condensates as a versatile platform for engineering macroscopic quantum superpositions and exploiting their twinning dynamics for precision measurements.