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Physica Scripta

Generating superpositions of quantum states via a beam splitter with position measurement

Gang Ren, Chunzao Zhang

Published Dec 19, 2023• 1 citation
Publisher

Abstract

Abstract We use the quadrature measurement to generate the novel nonclassical states via the beam splitter with two input states, i.e., a Fock state and a vacuum state. It is interesting to find that the desired target states are the Hermite polynomial excited vacuum states. Our results have shown that the zero-position detection for the position detector, the little photon number in the input state, and the high transmittance of the beam splitter (BS) are beneficial to improve the detection efficiency of finding the output states. The proposed states quantum statistical properties and squeezing effects are also studied in detail via different criteria. Our numerical analysis demonstrates that the output quantum states are new nonclassical states. Compared with the method of photon catalysis, position detection is easier to realize in experiments. Therefore, the results in this paper shall provide theoretical support for the experimental generation of several new nonclassical states.

DOI
10.1088/1402-4896/ad173c

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Abstract We use the quadrature measurement to generate the novel nonclassical states via the beam splitter with two input states, i.e., a Fock state and a vacuum state. It is interesting to find that the desired target states are the Hermite polynomial excited vacuum states. Our results have shown that the zero-position detection for the position detector, the little photon number in the input state, and the high transmittance of the beam splitter (BS) are beneficial to improve the detection efficiency of finding the output states. The proposed states quantum statistical properties and squeezing effects are also studied in detail via different criteria. Our numerical analysis demonstrates that the output quantum states are new nonclassical states. Compared with the method of photon catalysis, position detection is easier to realize in experiments. Therefore, the results in this paper shall provide theoretical support for the experimental generation of several new nonclassical states.
We present a scheme of quantum state truncation in the Fock basis (quantum scissors), based on the combined action of a nondegenerate optical parametric amplifier and a beam splitter. Differently from previously proposed linear-optics-based quantum scissors devices, which depend on reliable Fock state sources, our scheme requires only readily available Gaussian states, such as coherent state inputs (vacuum state included). A truncated state is generated after performing photodetections in the global state. We find that, depending on which output ports each of the two photodetectors is positioned, different types of truncated states may be produced: (i) states having a maximum Fock number of NNN, or (ii) states having a minimum Fock number NNN. In order to illustrate our method, we discuss an example having as input states a coherent state in the beam splitter and vacuum states in the amplifier, and show that the resulting truncated states display nonclassical properties, such as sub-Poissonian statistics and squeezing. We quantify the nonclassicality degree of the generated states using the Wigner-Yanase skew information measure. For complementarity, we discuss the efficiency of the protocol, e.g., generation probability as well as the effects of imperfections such as the detector's quantum efficiency and dark counts rate.
In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.
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.
Abstract We propose a method to generate an entangled squeezed state using an optical parametric amplifier (OPA) and a beam splitter (BS). This device can manipulate the output quantum light field by modulating two parameters: the intensity of the OPA and the transmittance of the optical BS. For the output quantum state associated with a symmetric BS, there is no quadrature squeezing. Moreover, neither photon correlation nor entanglement are observed. However, in terms of sum squeezing, the quantum state corresponding to the symmetric BS is the strongest. Therefore, an asymmetric BS and a highly squeezing OPA are the best choices for generating the quantum entangled squeezed states.
Abstract We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle an initial single-mode squeezed vacuum (SMSV) state with a photonic state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity and reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. The maximum hybrid entanglement is achieved at certain values of the squeezing and BS parameter, which can mean implementation of a two-qubit controlled − Z CZ − operation using the BS with appropriate initialization of the input states. The success probability of the gate, taking into account multiphoton outcomes in the measuring mode of the BS, is more than 0.3 . We also propose to use new continuous variable (CV) states of definite parity, which could increase the success probability of generating the maximum hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.
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.