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arXiv:quant-ph/0702126 · Physical Review A

Conditional generation of an arbitrary superposition of coherent states

Masahiro Takeoka, Masahide Sasaki

Published Jun 14, 2007• 41 citations
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Abstract

We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, even including realistic imperfections of the detectors, our scheme can generate a target state with a high fidelity. The amplitude of the generated states can be amplified by conditional homodyne detections.

DOI
10.1103/physreva.75.064302

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We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, even including realistic imperfections of the detectors, our scheme can generate a target state with a high fidelity. The amplitude of the generated states can be amplified by conditional homodyne detections.
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.
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 investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\ensuremath{\leqslant}4$, and conjecture that this can be generalized for an arbitrary nnn Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.
We propose a scheme for the conditional generation of arbitrary finite superpositions of Fock states in a single mode of a traveling optical field. The setup requires a source of squeezed vacuum states, beam splitters, strong coherent beams, photodetectors with single-photon sensitivity, and a final squeezer. If we want to generate a squeezed superposition of Fock states, which is sufficient in several applications, then the last squeezer is not even needed. The thrust of this method is that it achieves a high fidelity without requiring photodetectors with a high efficiency or a single-photon resolution. The possibility to improve its scaling by using a quantum memory is also discussed.
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.