Quantum metrology beyond Heisenberg limit with entangled matter wave solitons

Abstract

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.

Nonlinear quantum metrology with moving matter-wave solitons

“…3.1. Quantum field approach From the practical point of view it is more convenient to consider an interferometer consisting of two-mode condensate trapped in a double-well potential [23]. The Hamiltonian of the system under consideration is…”

“…Schrödinger picture is more suitable for the analysis of the system described by (18). Further we restrict ourselves by the Hartree approach justified in a large particle number limit [23]. The N-particle ground state vector, N Yñ | , can be written in this case as a product of N single-particle states…”

“…The set of equations (28) characterizes a model of interacting solitons in the presence of their motion, see [23,36]. This motion introduces some new important features which might be practically useful in the case of quantum measurement realization.…”

“…In [23] we examined weakly coupled one dimensional matter-wave bright solitons operating in a nonmoving regime. We have shown that soliton superposition, N00N-state, is formed in the limit of Schrödingercat state only under certain requirements on parameters of the system.…”

Nontrivial Attractors of the Perturbed Nonlinear Schrödinger Equation: Applications to Associative Memory and Pattern Recognition

“…[31,32] Furthermore, it was shown that matter wave bright solitons can form entangled states. [33] The addition of the dissipative terms allows one to control the velocity of a soliton such that it approaches zero. One of the key ingredients of our formulation is the particular form of the perturbative term which maintains the amplitude of the solution such that it does not decay to zero.…”