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Journal of the Optical Society of America B

Gain of squeezing via photon subtraction

Mikhail S. Podoshvedov, Sergey A. Podoshvedov, S. P. Kulik

Published Jun 23, 2025• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.558998

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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.
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 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 We introduce a new family of continuous variable (CV) states of definite parity originating from the single mode squeezed vacuum (SMSV) state by subtracting an arbitrary number of photons from it. A beam splitter with arbitrary transmittance and reflectance parameters redirects input photons in an indistinguishable manner to the output and measuring modes followed by probabilistic measurement, thereby converting the initial SMSV photon distribution into a new one after we know the number of registered photons. The family of the measurement-induced CV states is solely determined by the SMSV parameter which inevitably decreases when generating the CV states. We show that the quantum state engineering of CV states of definite parity by subtraction of multiphoton state from input SMSV state can significantly enhance their nonclassical properties (more squeezing, larger value of quantum Fisher information) compared to the initial state from which they originate, which, combined with a significant gain in brightness, makes them attractive for ultra-precise measurements. The potential of the new family of CV states of a certain parity, to which original SMSV, no doubt, belongs, can become decisive for a new push to implementation of optical quantum metrology protocols.
Abstract We introduce a family of new continuous variable (CV) states of definite parity originating from even single-mode squeezed vacuum (SMSV) state by subtracting an arbitrary number of photons from it. A beam splitter (BS) with arbitrary transmittance and reflectance parameters serves as a hub for redirecting input photons in an indistinguishable manner to the output and measuring modes followed by probabilistic measurement, thereby converting the initial SMSV photon distribution into new one after we know the number of registered photons in auхilliary mode. Depending on the parity of the subtracted photons, the family of the generated states is divided into two subfamilies, that is, into even and odd according to the parity of the Fock state subtracted. The family of the CV states is determined solely by one SMSV parameter, which inevitably decreases during their implementation. The algorithm of the quantum engineering can generate macroscopic CV states with a larger average number of photons (say, 4000 and even more) and quantum Fisher information of observable measuring the number of photons many times more (say, from tens of times for small practical values of the squeezing ratio to ≈4 for extremely high squeezing amplitude) than one of the original SMSV. The potential of the new family of the CV states of a certain parity, to which original SMSV, no doubt, belongs, can become decisive for a new push to implementation of optical quantum metrology protocols.
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.