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Laser Physics

Quantum phase estimation for nonlinear phase shifts with entangled spin coherent states of two modes

K. Berrada, S. Abdel‐Khalek

Published Aug 20, 2013• 12 citations
Publisher

Abstract

Recently, we presented (Berrada K, Abdel-Khalek S and Raymond Ooi C H 2012 Phys. Rev. A 86 033823) an improved phase estimation scheme employing entangled spin coherent states (ESCSs) using the Holstein?Primakoff realization of angular momentum algebra. Here, we study the nonlinear phase enhancement from a generalized nonlinearity on ESCSs under perfect and lossy conditions with the same mean photon number and nonlinearity order. The results show that an increase in the spin number gives the smallest variance in the phase parameter in comparison to N00N states for different orders of nonlinearity. Finally, we study the physical properties of the input optical field and explore a connection between this quantity and the output state phase uncertainty. In particular, we show that the Mandel parameter may be used as an indicator of the phase estimation behavior in this interferometric setting.

DOI
10.1088/1054-660x/23/10/105201

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Recently, we presented (Berrada K, Abdel-Khalek S and Raymond Ooi C H 2012 Phys. Rev. A 86 033823) an improved phase estimation scheme employing entangled spin coherent states (ESCSs) using the Holstein?Primakoff realization of angular momentum algebra. Here, we study the nonlinear phase enhancement from a generalized nonlinearity on ESCSs under perfect and lossy conditions with the same mean photon number and nonlinearity order. The results show that an increase in the spin number gives the smallest variance in the phase parameter in comparison to N00N states for different orders of nonlinearity. Finally, we study the physical properties of the input optical field and explore a connection between this quantity and the output state phase uncertainty. In particular, we show that the Mandel parameter may be used as an indicator of the phase estimation behavior in this interferometric setting.
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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.
Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\ensuremath{\propto}1/N$ scaling of precision (NNN is the mean photon number of the light field). But when NNN is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the 1/N1/21/{N}^{1/2}1/N1/2 (1/N3/21/{N}^{3/2}1/N3/2) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schr\"odinger-cat states can be used to reach the 1/N1/N1/N scaling for the linear phase and 1/N21/{N}^{2}1/N2 scaling for the nonlinear phase.
Abstract We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
We investigate the phase enhancement of quantum states subject to nonlinear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states with the same average particle number $\ensuremath{\langle}n\ensuremath{\rangle}$ and nonlinearity exponent kkk. We investigate the creation of an approximate entangled coherent state (AECS) from a photon-subtracted squeezed vacuum with current optical technology methods and show that a pure AECS is even better than an even ECS for large $\ensuremath{\langle}n\ensuremath{\rangle}$. Finally, we examine the simple, but physically relevant, cases of loss in the nonlinear interferometer for a fixed average photon number $\ensuremath{\langle}n\ensuremath{\rangle}$.