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arXiv:1511.06531 · Physica Scripta

Conditional generation of optical Schrödinger cat states

Петер Адам, T. Kiss, Z. Darázs, Igor Jex

Published Sep 1, 2010• 7 citations
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Abstract

Given a source of two coherent state superpositions with small separation in a travelling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origin of the phase space. The separation of coherent states in the superposition will be amplified during the process.

DOI
10.1088/0031-8949/2010/t140/014011

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Given a source of two coherent state superpositions with small separation in a travelling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origin of the phase space. The separation of coherent states in the superposition will be amplified during the process.
We propose a scheme to prepare optical Schrödinger-cat states in a traveling wave setting. Two states are similarly prepared via the self-Kerr effect and after mixing them, one mode is measured by homodyne detection. In the other mode a superposition of coherent states is conditionally prepared. The advantage of the scheme is that assuming a small Kerr effect one can prepare with high probability one from a set of Schrödinger-cat states. The measured value of the quadrature provides the information, which state from the set is actually prepared.
Superpositions of macroscopically distinct quantum states, introduced in Schrödinger’s famous Gedankenexperiment, are an epitome of quantum “strangeness” and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrödinger’s cat — the superposition of two opposite-amplitude coherent states — is also the backbone of quantum information processing in the continuous-variable domain. Here we implement two protocols for producing and amplifying optical Schrödinger’s cats. In the first protocol we remotely prepare a high-efficiency Schrödinger cat state by applying the remote state preparation to a N00N state prepared between two parties that are separated by a lossy medium. The second protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. The latter technique enables implementation in an iterative manner, in principle allowing creation of Schrödinger’s cat states of arbitrarily high amplitude.
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.
A "Schrödinger cat" state of free-propagating light can be defined as a quantum superposition of well separated coherent states. 1, 2 We demonstrated, theoretically and experimentally, a protocol which allows to generate arbitrarily large squeezed Schrödinger cat states, using a homodyne detection and photon number states as resources. We implemented this protocol experimentally with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly presents several quantum phase-space interference fringes between the "dead" and "alive" components, and it is large enough to become useful for experimental tests of quantum theory and quantum information processing.
Coherent state superpositions, also known as Schrödinger cat states, are widely recognized as promising resources in quantum information, quantum metrology, as well as fundamental tests. These states are hard to produce deterministically and most schemes for their probabilistic generation can only attain amplitudes too small for practical use. This is for example the case for photon-subtracted squeezed vacuum (PSSV), which can be used to approximate cat states of amplitude no larger than y = 1.5 if the fidelity is to be maintained above 95%. One way to reach larger amplitudes is to start with pairs of small cats and then to interfere them on a balanced beam splitter. The projective measurement of one of the outputs is used to herald a larger cat resulting from the constructive interference of the initial states. The scheme proposed here uses the projection |x = 0〉〈x = 0| as the heralding condition. Homodyning is proposed, as opposed to photon counting, because homodyne detection has high a quantum efficiency, and - as demonstrated in the paper - can be tuned to increase the success probability of the amplification without heavily compromising the output's fidelity.