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arXiv:2312.14643 · Physical Review A

Generation of squeezed Fock states by measurement

S. B. Korolev, E. N. Bashmakova, Alexander K. Tagantsev, T. Yu. Golubeva

Published May 16, 2024• 11 citations
arXivHTMLPDF

Abstract

The generation of squeezed Fock states by the one or more photon subtraction from a two-mode entangled Gaussian (TMEG) state is theoretically addressed. We showed that an arbitrary order Fock state can be generated this way and we obtained a condition that should be imposed on the parameters of the TMEG state to guarantee such a generation. We called the regime, in which this condition is satisfied, the universal solution regime. We showed that, for the first squeezed Fock state, the above condition is redundant such that the generation of the first squeezed Fock state is still possible by a one-photon subtraction from an arbitrary TMEG state. At the same time, the maximum generation probability of the first squeezed Fock state generation corresponds to the universal solution regime. We applied the above results to the description of generation of the squeezed Fock states using a beam splitter and a controlled-Z operation. We have estimated the parameters of such setups and input squeezed states, which are necessary to obtain squeezed Fock states with the maximum probability.

DOI
10.1103/physreva.109.052428

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The generation of squeezed Fock states by the one or more photon subtraction from a two-mode entangled Gaussian (TMEG) state is theoretically addressed. We showed that an arbitrary order Fock state can be generated this way and we obtained a condition that should be imposed on the parameters of the TMEG state to guarantee such a generation. We called the regime, in which this condition is satisfied, the universal solution regime. We showed that, for the first squeezed Fock state, the above condition is redundant such that the generation of the first squeezed Fock state is still possible by a one-photon subtraction from an arbitrary TMEG state. At the same time, the maximum generation probability of the first squeezed Fock state generation corresponds to the universal solution regime. We applied the above results to the description of generation of the squeezed Fock states using a beam splitter and a controlled-Z operation. We have estimated the parameters of such setups and input squeezed states, which are necessary to obtain squeezed Fock states with the maximum probability.
Subject of study. Schemes for generating non-Gaussian quantum states and the states required for quantum error correction protocols are investigated. Aim of study. The primary objectives were to generalize methods and approaches for describing the generation of non-Gaussian states in measurement schemes to determine the most effective model for describing the generation process and to assess a model for generating squeezed Fock states and a quantum error correction code based on such states. Method. A theoretical analysis of the wavefunction evolution of various non-Gaussian states in particle-number measurement schemes was performed; in this analysis, squeezed states were used as inputs. Main results. A scheme for generating squeezed Fock states was theoretically examined. An explicit analytical expression for the output wavefunction was constructed to completely analyze the output states depending on the parameters of the scheme under consideration. A set of conditions imposed on the parameters of a two-mode entangled Gaussian state, i.e., the “universal solution regime,” was outlined. This regime guaranteed the generation of squeezed Fock states with a high probability. Practical significance. The results demonstrated the ability of the universal solution regime to generate squeezed Fock states of arbitrary order for a given squeezing parameter. The feasibility of using squeezed Fock states in quantum error correction codes was analyzed. A comparative study of squeezed Fock states and squeezed Schrödinger cat states as codewords confirmed squeezed Fock states as robust solutions to ensure information protection in channels subjected to particle loss and dephasing.
We investigate the generation of squeezed Fock states (SFSs) via particle-number measurements in the modes of multimode Gaussian states. We identify a universal class of NNN-mode Gaussian states for which measuring N−1N-1N−1 modes results in the generation of SFSs. The key feature of these states is that the generated SFSs depend only on the total number of detected particles and are independent of their distribution among the detectors. Based on the general form of the wave functions of multimode Gaussian states, we propose a universal scheme for SFS generation. For this scheme, we evaluate the probability of SFS generation and analyze the robustness of the process against imperfections in particle-number-resolving detectors. In addition, we compare the universal scheme with a nonuniversal scheme, in which the generation of SFSs depends on a specific distribution of particle numbers across the detectors. We demonstrate that the universal scheme provides a higher probability of SFS generation, at the cost of increased experimental resources.
Abstract We investigate the generation of squeezed Fock states (SFSs) via particle-number measurements in the modes of multimode Gaussian states. We identify a universal class of N -mode Gaussian states for which measuring N − 1 modes results in the generation of SFSs. The key feature of these states is that the generated SFSs depend only on the total number of detected particles and are independent of their distribution among the detectors. Based on the general form of the wave functions of multimode Gaussian states, we propose a universal scheme for SFS generation. For this scheme, we evaluate the probability of SFS generation and analyze the robustness of the process against imperfections in particle-number-resolving detectors. In addition, we compare the universal scheme with a nonuniversal scheme, in which the generation of SFSs depends on a specific distribution of particle numbers across the detectors. We demonstrate that the universal scheme provides a higher probability of SFS generation, at the cost of increased experimental resources.
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.
Conditional Measurement scheme which employs linear optical elements and photon detection is the fertile ground for nonclassical state generation. We consider a simple setup that requires a coherent state and a number state as inputs of the beam splitter, and a photon detector. We show that by tuning the parameters involved in the setup, we can achieve optimal squeezing from the setup. This is facilitated by writing the output state of the conditional measurement as displaced qudits. Setting aside displacement which plays no role in squeezing, the finite-dimensional representation makes it possible to calculate the maximal amount of squeezing. By fixing the detection at one photon level irrespective of any number state input and carefully chosen coherent parameter and beam splitter reflectivity values, one can reach the maximal squeezing at least for lower number state inputs. This is in contrast to the earlier attempts in atom field interaction models etc., where the squeezing obtained was far from saturation. To accommodate the experimental imperfections, we consider the impure nature of the photon source and detector inefficiency.
The paper considers the possibility of generating different non-Gaussian states using the entangled state photon measurement scheme. In the paper, we have proposed a way to explicitly find the wave function and the Wigner function of the output state of this scheme. Moreover, the solutions found are not restricted to any particular case, but have maximum generality (depend on the number of measured photons and on all parameters of the scheme). Such a notation allowed us to carry out a complete analysis of the output states, depending on the scheme parameters. Using explicit expressions, we have analyzed the magnitude of non-Gaussianity of the output states, and we have revealed which particular states can be obtained in the proposed scheme. We have considered in detail a particular case of measurement (single photon measurement) and have shown that using explicit expressions for the output state wave function one can find scheme parameters to obtain states suitable for quantum error correction codes with a large fidelity value and high probability. The Schrodinger cat state with amplitude α=2α=2α=2 can be obtained with fidelity F≈0.88F \approx 0.88F≈0.88 and probability 18 percent, and the squeezed Schrodinger cat state (α=0.5α=0.5α=0.5, R=1R=1R=1) with fidelity F≈0.98F \approx 0.98F≈0.98 and probability 22 percent.