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arXiv:2108.03408 · Physical Review A

Enhanced nonlinear quantum metrology with weakly coupled solitons in the presence of particle losses

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

Published Jan 18, 2022• 16 citations
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Abstract

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. Commonly, an unavoidable lossy effect is believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for estimation of phase parameters at the Heisenberg (up to $1/N$) and super-Heisenberg (up to $1/{N}^{3}$) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is a soliton Josephson junction (SJJ) system, which provides the formation of the quantum probe, the entangled Fock (NOON-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible for both the linear and nonlinear metrologies with the SJJs and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

DOI
10.1103/physreva.105.012606

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The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. Commonly, an unavoidable lossy effect is believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for estimation of phase parameters at the Heisenberg (up to 1/N1/N1/N) and super-Heisenberg (up to 1/N31/{N}^{3}1/N3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is a soliton Josephson junction (SJJ) system, which provides the formation of the quantum probe, the entangled Fock (NOON-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible for both the linear and nonlinear metrologies with the SJJs and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.
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.
We consider a multiparameter quantum metrology problem with bright soliton networks in the presence of weak losses. We introduce the general Heisenberg limit (GHL) ${\ensuremath{\sigma}}_{\mathbit{\ensuremath{\chi}}}=1/{N}^{k}$ that characterizes fundamental limitations for unknown parameter measurement and estimation accuracy ${\ensuremath{\sigma}}_{\mathbit{\ensuremath{\chi}}}$ within linear (k=1k=1k=1) and nonlinear (k=3k=3k=3) quantum metrology approaches to solitons. We examine multipartite NOON states specially prepared for the improvement of multiparameter estimation protocols. As a particular example of producing such states, we propose a three-mode soliton Josephson-junction (TMSJJ) model as a three-mode extension for the soliton Josephson-junction bosonic model, which we previously proposed. The energy spectrum of the TMSJJ exhibits sharp phase transition peculiarities for the TMSJJ ground state. The transition occurs from a Gaussian-like (coherent) state to the superposition of entangled Fock states, which rapidly approach the three-mode NOON state. We show that in the presence of weak losses the TMSJJ enables saturation scaling relevant to the optimal state limit close to the GHL. Our findings open prospects for quantum network sensorics with atomtronic circuits.
Abstract The Josephson junctions (JJs) are at the heart of modern quantum technologies and metrology. In this work we establish quantum features of an atomic soliton Josephson junction (SJJ) device, which consists of two weakly-coupled condensates with negative scattering length. The condensates are trapped in a double-well potential and elongated in one dimension. Starting with classical field theory we map for the first time a two-soliton problem onto the effective two-mode Hamiltonian and perform a second quantization procedure. Compared to the conventional bosonic Josephson junction condensate system, we show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number, N 2. A novel self-tuning effect for the effective tunneling parameter is also demonstrated in the SJJ-model, which depends on the particle number and rapidly vanishes as the JJ population imbalance increases. The formation of entangled Fock state superposition is predicted for the quantum SJJ-model, revealing dominant N00N-state components at the ‘edges’ for n = 0, N particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present in the vicinity of the major N00N-state component. This peculiarity of the quantum SJJ-model establishes an important difference from its semiclassical analogue obtained in the framework of Hartree approach. Our results are confirmed by studying the first and N-order Hillery–Zubairy criteria applied for studying multiparticle entanglement and planar spin squeezing. The Einstein–Podolsky–Rosen quantum steering represents an important prerequisite for the crossover to the mesoscopic superposition Schrödinger-cat and/or N00N-states. The feasibility in observation for these predicted states of the SJJ-model in the experiments is also discussed by taking into account one- and three-body losses for lithium condensates.
We present an improved phase estimation scheme employing entangled SU(1,1) coherent states in comparison to NOON and entangled coherent states under perfect and lossy conditions for a fixed mean photon number. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized nonlinearity of the phase shifts, both without and with losses. Furthermore, we show that these states give the smallest variance in the phase parameter for a large number of photons in a different order of nonlinearity. Finally, the phase sensitivity of this interferometric setting with parity detection is discussed.
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.