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arXiv:2412.19164

Squeezing in conditional measurement setup with coherent input

Devibala Esakkimuthu, Basherrudin Mahmud Ahmed A

Published Dec 26, 2024• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2412.19164

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Physica Scripta•Dec 19, 2023•1 citation
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.
Abstract Conditional measurement schemes, which employ linear optical elements and photon detectors, have recently become powerful tools for generating and enriching nonclassical states in single- and multi-mode scenarios. Here, the nonclassical resourcefulness of a simple single-mode conditional measurement (CM) setup, with a coherent state as one input state, is examined. Studying the output of this setup in the form of displaced qudits (DQ) simplifies the complete characterization of nonclassical resources. The figures of merit of the prepared states are evaluated through quadrature squeezing and some of the non-Gaussian measures such as the Hilbert–Schmidt distance, the quantum relative entropy and the Wigner negativity to identify the squeezing and non-Gaussianity of the states, respectively. The squeezing capacity of the DQ output is compared with the achievable squeezing in finite superposed Fock states, since DQ also constitute a finite-dimensional representation. This optimal squeezing is attained when the detector detects the single photons in the CM setup. All the studied non-Gaussian measures confirm the qualitative agreement that the non-Gaussianity of the setup is limited and does not exceed that of the input number state. The interplay of nonclassical resources between non-Gaussianity and squeezing is exemplified, showing that states exhibiting non-Gaussianity do not exhibit squeezing, and vice versa. In addition, experimental imperfections, such as photon-source impurities and detector inefficiencies, are accommodated to analyze the realistic preparation of DQ. The calculated success probabilities are around 15 % to create the maximally squeezed states under experimental conditions. It demonstrates the potential of nonclassical state generation with minimal nonclassical inputs through the CM scheme.
Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology through examples of generation of single-mode states with two and three heralding modes, and generation of two-mode states with two heralding modes.
The article shows that a single photon source and straightforward, purely optical processes can be used to produce a linear superposition of two macroscopically identifiable optical coherent states. A superposition of coherent states in a freely propagating optical field with high coherence amplitude can be generated via weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detection with imperfect threshold detectors. (α>2) and F=0.99, which is extremely precise. Our technique does not require a precise photon count, resolving measurements, or nonlinear Kerr-type interactions, in contrast to all existing schemes for obtaining such a state. It also exhibits some tolerance to inefficiencies in photon generation and is robust against detection of inefficiencies.
In this Letter, we present a simple and versatile scheme for enhancing the nonclassical properties of light states using only linear optics and photodetectors. By combining a coherent state |α〉 and an arbitrary pure state of light |ϕ〉 (excluding coherent states) at two beam splitters, we show that the amplitude α of the coherent state can be tuned to filter out specific Fock components and generate states of light with increased nonclassical features. We provide two examples of input states and demonstrate the effectiveness of our scheme in enhancing the sub-Poissonian statistics or the quadrature squeezing of the output states.
Creation of high fidelity photonic quantum states in the continuous variable regime is indispensable for the implementation of quantum technologies universally. However, this is a challenging task as it requires higher nonlinearity or larger Fock states. In this article, we surmount this necessity by using a linear optical setup with a cascaded arrangement of beam splitters that relies solely on single photon sources and single photon detectors to tailor desired single mode nonclassical states. To show the utility of this setup, we demonstrate the generation of displaced higher photon states with unit fidelity and the family of Schrodinger cat states above 98%98\%98% fidelity. In addition, we manifest the generation of GKP resource states, such as ON states and weak cubic phase states with 99%99\%99% fidelity. Creating such a variety of important states in this single setup is made feasible by stating the output in the form of displaced qudits. This figure of merit facilitates efficient identification and optimization of input parameters required to generate the target single mode quantum states. We also account for the experimental imperfections by incorporating detector inefficiencies and non-unit single photon sources. This cascaded setup will assist the experimentalists to explore the feasible creation of target states using currently available resources, such as single photon sources and single photon detectors.
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.