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Physical Review A

Approximate phase-coherent states and their generation

Christopher C. Gerry, Trung Bui

Published Sep 22, 2009• 4 citations
Publisher

Abstract

We show that phase-coherent states of a single-mode quantized electromagnetic field are well approximated by certain superpositions of the squeezed vacuum and one-photon states. We further show that the squeezed vacuum and one-photon states can be understood, approximately, as superpositions of phase-coherent states. Our approximate phase-coherent states may be generated by a degenerate parametric down-converter acting on a prepared input state of the form $|0⟩+\ensuremath{\alpha}|1⟩$. The input superposition state itself can be prepared from a coherent state $|\ensuremath{\alpha}⟩$ by a quantum scissors device.

DOI
10.1103/physreva.80.033831

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We show that phase-coherent states of a single-mode quantized electromagnetic field are well approximated by certain superpositions of the squeezed vacuum and one-photon states. We further show that the squeezed vacuum and one-photon states can be understood, approximately, as superpositions of phase-coherent states. Our approximate phase-coherent states may be generated by a degenerate parametric down-converter acting on a prepared input state of the form ∣0⟩+\ensuremathα∣1⟩|0⟩+\ensuremath{\alpha}|1⟩∣0⟩+\ensuremathα∣1⟩. The input superposition state itself can be prepared from a coherent state ∣\ensuremathα⟩|\ensuremath{\alpha}⟩∣\ensuremathα⟩ by a quantum scissors device.
We propose a realizable experimental scheme to prepare superposition of the vacuum and one-photon states by truncating an input coherent state. The scheme is based on the quantum scissors device proposed by Pegg, Phillips, and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] and uses photon-counting detectors, a single photon source, and linear optical elements. Realistic features of the photon counting and single-photon generation are taken into account and possible error sources are discussed together with their effect on the fidelity and efficiency of the truncation process. Wigner function and phase distribution of the generated states are given and discussed for the evaluation of the proposed scheme.
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
We present the generation of approximated coherent state superpositions—referred to as Schrödinger cat states—by the process of subtracting single photons from picosecond pulsed squeezed states of light. The squeezed vacuum states are produced by spontaneous parametric down-conversion (SPDC) in a periodically poled KTiOPO4 crystal while the single photons are probabilistically subtracted using a beamsplitter and a single photon detector. The resulting states are fully characterized with time-resolved homodyne quantum state tomography. Varying the pump power of the SPDC, we generated different states which exhibit non-Gaussian behavior.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear χ2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong χ3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
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