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arXiv:0708.1956 · Physical Review A

Transforming squeezed light into a large-amplitude coherent-state superposition

Anne E. B. Nielsen, Klaus Mølmer

Published Oct 26, 2007• 27 citations
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Abstract

A quantum superposition of two coherent states of light with small amplitude can be obtained by subtracting a photon from a squeezed vacuum state. In experiments this preparation can be made conditioned on the detection of a photon in the field from a squeezed light source. We propose and analyze an extended measurement strategy which allows generation of high fidelity coherent state superpositions with larger amplitude.

DOI
10.1103/physreva.76.043840

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A quantum superposition of two coherent states of light with small amplitude can be obtained by subtracting a photon from a squeezed vacuum state. In experiments this preparation can be made conditioned on the detection of a photon in the field from a squeezed light source. We propose and analyze an extended measurement strategy which allows generation of high fidelity coherent state superpositions with larger amplitude.
We study how photon addition and subtraction can be used to generate squeezed superpositions of coherent states (SSCSs) in free-traveling fields with high fidelities and large amplitudes. It is shown that an arbitrary NNN-photon subtraction results in the generation of a SSCS with nearly the perfect fidelity (F>0.999)(F>0.999)(F>0.999) regardless of the number of photons subtracted. In this case, the amplitude of the SSCS increases as the number of the subtracted photons gets larger. For example, two-photon subtraction from a squeezed vacuum state of 6.1dB6.1\phantom{\rule{0.3em}{0ex}}\mathrm{dB}6.1dB can generate a SSCS of $\ensuremath{\alpha}=1.26$, while in the case of the four-photon subtraction a SSCS of a larger amplitude $\ensuremath{\alpha}=1.65$ is obtained under the same condition. When a photon is subtracted from a squeezed vacuum state and another photon is added subsequently, a SSCS with a lower fidelity $(F\ensuremath{\approx}0.96)$ yet higher amplitude $(\ensuremath{\alpha}\ensuremath{\approx}2)$ can be generated. We analyze some experimental imperfections including inefficiency of the detector used for the photon subtraction.
We have created heralded coherent-state superpositions (CSSs) by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This experiment is enabled by and utilizes the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean-photon number of $2.{75}_{\ensuremath{-}0.24}^{+0.06}$ and a fidelity of $0.{59}_{\ensuremath{-}0.14}^{+0.04}$ with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs.
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It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude $(\ensuremath{\alpha}>2)$ and high fidelity (F>0.99)(F>0.99)(F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.
We propose two experimental schemes for producing coherent-state superpositions which approximate different nonclassical states conditionally in traveling optical fields. Although these setups are constructed of a small number of linear optical elements and homodyne measurements, they can be used to generate various photon number superpositions in which the number of constituent states can be higher than the number of measurements in the schemes. We determine numerically the parameters to achieve maximal fidelity of the preparation for a large variety of nonclassical states, such as amplitude squeezed states, binomial states, squeezed cat states, and various photon number superpositions. The proposed setups can generate these states with high fidelities and with success probabilities that can be sufficient for practical applications.