We study sensitivity of phase estimation of Mach-Zehnder (MZ) interferometer with original two-mode squeezed vacuum (TMSV) state. At the initial stage, the TMSV state is converted into two single-mode squeezed vacuum (SMSV) states, from each of which photons are subtracted by measurement by photon-number resolving (PNR) detector in auxiliary modes. New measurement-induced continuous variable (CV) states of a certain parity can already demonstrate gain sensitivity more than 20 dB in relation to the initial SMSV states at the output from the MZ interferometer and follow to Heisenberg scaling in the case of subtracting a large number of photons in the measuring channels for practical values of the SMSV squeezing 5 dB>. Using only one measurement-induced CV state of a certain parity together with the SMSV state shows an increase in sensitivity of no more than 11 dB. We show that the sensitivity of the phase estimation obtained by measuring the intensity difference of two measurement-induced CV states in two arms of the MZ interferometer can surpass quantum Cramer-Rao (QCR) boundary of the original two SMSV states just in the practical range of input squeezing 5 dB>. In general, the strategy with preliminary subtraction of photons from two SMSV enables greatly enhance the sensitivity of the MZ interferometer in the practical case of small values of squeezing.
We study sensitivity of phase estimation of Mach-Zehnder (MZ) interferometer with original two-mode squeezed vacuum (TMSV) state. At the initial stage, the TMSV state is converted into two single-mode squeezed vacuum (SMSV) states, from each of which photons are subtracted by measurement by photon-number resolving (PNR) detector in auxiliary modes. New measurement-induced continuous variable (CV) states of a certain parity can already demonstrate gain sensitivity more than 20 dB in relation to the initial SMSV states at the output from the MZ interferometer and follow to Heisenberg scaling in the case of subtracting a large number of photons in the measuring channels for practical values of the SMSV squeezing 5 dB>. Using only one measurement-induced CV state of a certain parity together with the SMSV state shows an increase in sensitivity of no more than 11 dB. We show that the sensitivity of the phase estimation obtained by measuring the intensity difference of two measurement-induced CV states in two arms of the MZ interferometer can surpass quantum Cramer-Rao (QCR) boundary of the original two SMSV states just in the practical range of input squeezing 5 dB>. In general, the strategy with preliminary subtraction of photons from two SMSV enables greatly enhance the sensitivity of the MZ interferometer in the practical case of small values of squeezing.
Abstract The phase sensitivity of a Mach–Zehnder (MZ) interferometer with a two-mode squeezed vacuum (TMSV) probe state is studied. At the initial stage, the TMSV state is deterministically converted into two single-mode squeezed vacuum (SMSV) states, from each of which photons are subtracted via photon-number resolving measurement in auxiliary measurement modes. The new probe state can already demonstrate gain sensitivity of more than 20 dB with input squeezing of 5 dB and follow Heisenberg scaling. The phase sensitivity of the MZ interferometer, estimated by measuring the intensity difference of two measurement-induced continuous variable states, can surpass the ultimate one with SMSV probe states, at least, with squeezing less than 5 dB. In general, the strategy with preliminary subtraction of photons significantly increases the estimate potential of weakly squeezed states as the probe in MZ phase-dependent interferometry; in particular, it is more effective compared to generating highly squeezed TMSV states or SMSV states.
Quantum Cramer-Rao (QCR) bound is attached to a particular nonclassical state, therefore appropriate choice of the probe state is of the key importance to enhance sensitivity beyond classical one. Since the work of C.M. Caves (Phys. Rev. D 23 1693 (1981)) Mach-Zehnder (MZ) interferometry operates with single-mode squeezed vacuum (SMSV) light coupled with a coherent state. We report the gain sensitivity of the phase-dependent MZ interferometer by more than 10 dB compared to the original result (Phys. Rev. Lett. 100, 073601 (2008)) by using SMSV state with squeezing <10 dB from which a certain number of photons was initially subtracted. The gain sensitivity is also observed when measuring the difference of output intensities of the SMSV state with squeezing <3 dB from which 2,4,6 photons are subtracted and large coherent state. Overall, subtracting photons from the initially weakly squeezed light can prove to be a more efficient strategy in the quantum MZ interferometry compared to highly squeezed SMSV state generation.
Abstract Choice of the quantum probe state is of key importance to enhance the sensitivity of the Mach–Zehnder (MZ) interferometer beyond the classical one and even approach the quantum Cramér–Rao bound. According to the work of Caves (Caves 1981 Phys. Rev. D 23 1693), the quantum MZ interferometer is a phase-dependent one operating with single-mode squeezed vacuum (SMSV) light coupled with a coherent state. We use the SMSV state with squeezing <10 dB and report a gain in sensitivity of the phase-dependent MZ interferometer of more than 10 dB compared to the original result (Pezze and Smerzi 2008 Phys. Rev. Lett. 100 073601) via photon subtraction. The gain in sensitivity is also observed when measuring the difference in output intensities of the SMSV state with squeezing of < 3 dB from which two, four, and six photons are subtracted and a large coherent state. Overall, subtracting photons from the initially weakly squeezed light can prove to be a more efficient strategy in quantum MZ interferometry compared to highly squeezed SMSV state generation.
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.
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 develop a method to generate nonclassical light with a larger quadrature squeezing than one of the single-mode squeezed vacuum (SMSV) states by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more than 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ∼5dB, and less quadrature variance. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with nonunit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal measurement of photons in the auxiliary mode. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of an odd number of photons (say, 3 photons) in auxiliary mode allows the implementation of the measurement-induced even CV state, which is several times brighter than the initial state, has lower quadrature noise, and is generated with greater probability.