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中国物理B：英文版

Quantum interferometer with two-mode squeezed vacuum：_^z2 measurement

张渊明, 李昕伟, 金光日

Published Jan 1, 2013• 0 citations
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Abstract

Quantum interferometric strategy with input two-mode squeezed vacuum[Phys.Rev.Lett.104 103602]is reexamined for both parity and S_z~2 measurements.Unlike the previous scheme,we find that phase sensitivity obtained with the S_z~2 measurement is minimized at phase origin,which may be useful to estimate a small phase shift at high precision.For the phase deviated from zero,the sensitivity increases more slowly than that of the parity detection.

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Quantum interferometric strategy with input two-mode squeezed vacuum[Phys.Rev.Lett.104 103602]is reexamined for both parity and S_z2 measurements.Unlike the previous scheme,we find that phase sensitivity obtained with the S_z2 measurement is minimized at phase origin,which may be useful to estimate a small phase shift at high precision.For the phase deviated from zero,the sensitivity increases more slowly than that of the parity detection.
Quantum metrology is to estimate accurately the value of an unknown parameter with the assistance of the quantum effects, in order to break through the standard quantum limit, even reach the Heisenberg limit. In this work, we study the performance of a general photon-added two-mode squeezed vacuum state that is taken as a detection state of a Mach-Zehnder interferometer. Based on quantum Fisher information, within the constraint on the total mean photon number, symmetric and asymmetric photon addition cannot improve the ultimate phase sensitivity. However, for a given initial squeezing parameter, on this occasion, the symmetric and asymmetric photon addition can improve the ultimate phase sensitivity. Compared with the asymmetric photon-added two-mode squeezed vacuum state, the symmetric one can well improve the ultimate phase sensitivity. This may be because it is always better to implement the symmetric photon addition rather than the asymmetric one in order to increase the mean photon number of the resulting state. On the other hand, via parity detection, the symmetric and asymmetric photon-added two-mode squeezed vacuum state can indeed improve the phase sensitivity of a Mach-Zehnder interferometer for a given initial squeezing parameter. Based on the parity detection, within a constraint on the mean photon number, although the two-mode squeezed vacuum state can give the better phase sensitivity at the optimal phase shift (φ = 0), the phase sensitivity offered by the symmetric and asymmetric photon-added two-mode squeezed vacuum states are both more stable around φ = 0 than by the two-mode squeezed vacuum state. In addition, we show that for the symmetric photon-added two-mode squeezed vacuum state, parity detection is an optimal detection only when the optimal phase shift approaches to zero. When the phase shift slightly deviates from zero, the parity detection is not an optimal detection scheme. Finally, for all values of the phase shift, our results also clearly show that the parity detection is not an optimal detection scheme for the asymmetric photon-added two-mode squeezed vacuum state serving as an interferometer state.
We investigate the sensitivity of phase estimation in a Mach–Zehnder interferometer with photon-subtracted two-mode squeezed vacuum states. Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér–Rao bound (i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction. On the other hand, the quantum Cramér–Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states. In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse. Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.
We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach–Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ = 0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramér–Rao bound can be approached with the parity detection.
We study the application of photon-subtracted two-mode squeezed vacuum states (TMSVS), where identical photon numbers are subtracted from each beam, to the problem of quantum optical interferometry with the photon-number parity measurements scheme. Previously, Anisimov et al. [Phys. Rev. Lett.104, 103602 (2010)] have studied the prospect of using the TMSVS for parity measurements based interferometry. However, the joint photon number distribution of this state before beam splitting is thermal-like in each mode, meaning that its statistics are super-Poissonian and that the most probable state of the field is the double vacuum and that the average photon number is low. Furthermore, with these states the sensitivity of the phase-shift measurement is extremely sensitive to the size of the phase shift to be measured for large average photon numbers. The simultaneous subtraction of 1, 2, or 3 photons from each mode has the effects of increasing the average photon numbers of each mode and rendering the statistics nearly Poissonian and in some cases sub-Poissonian. We show that phase uncertainties for such states are less sensitive to the phase shift itself at large average photon numbers. We also show that the photon-subtracted TMSVS also lead to increased resolution.