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arXiv:1808.00234 · Journal of the Optical Society of America B

Efficient amplification of superpositions of coherent states using input states with different parities

Changhun Oh, Hyunseok Jeong

Published Oct 29, 2018• 8 citations
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Abstract

We investigate an experimentally feasible scheme for amplification of superpositions of coherent states (SCSs) in light fields. This scheme mixes two input SCSs at a 50:50 beam splitter and performs postselection by a homodyne detection on one output mode. The key idea is to use two different types of SCSs with opposite parities for input states, which results in an amplified output SCS with a nearly perfect fidelity.

DOI
10.1364/josab.35.002933

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We investigate an experimentally feasible scheme for amplification of superpositions of coherent states (SCSs) in light fields. This scheme mixes two input SCSs at a 50:50 beam splitter and performs postselection by a homodyne detection on one output mode. The key idea is to use two different types of SCSs with opposite parities for input states, which results in an amplified output SCS with a nearly perfect fidelity.
We present a simple protocol to purify a coherent-state superposition that has undergone a linear lossy channel. The scheme constitutes only a single beam splitter and a homodyne detector, and thus is experimentally feasible. In practice, a superposition of coherent states is transformed into a classical mixture of coherent states by linear loss, which is usually the dominant decoherence mechanism in optical systems. We also address the possibility of producing a larger amplitude superposition state from decohered states, and show that in most cases the decoherence of the states are amplified along with the amplitude.
We present a simple protocol to purify a coherent state superposition from a statistical mixture of a superposed states and coherent states. The scheme constitutes only a single beam splitter and a homodyne detector, and thus experimentally feasible. In practice, a superposition of coherent states is transformed into such a mixture by linear loss, which is usually the dominant decoherence mechanism in optical systems. We also address the possibility of producing a larger amplitude superposition state from decohered states, and show that in most cases the decoherence of the states are amplified along with the amplitude.
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.
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.
We compare two amplification schemes, photon addition and then subtraction ( a ̂ a ̂ † ) and successive photon addition ( a ̂ † 2 ), applied to hybrid entangled states (HESs) and superpositions of coherent states (SCSs). We show that the fidelity and gain of the amplification schemes for HESs are the same as those of coherent states. However, SCSs show quite nontrivial behavior by the amplification schemes, depending on the amplitudes of coherent states, the number of coherent-state components, and the relative phases between the components. This implies that appropriate amplification schemes for SCSs should be chosen depending on the tasks and specific forms of the states. To investigate the quality of amplified states, we calculate the quantum Fisher information, a measure of quantum phase estimation. In terms of the quantum Fisher information, the a ̂ a ̂ † scheme tends to show better performance for relatively small amplitudes ( α ≲ 0.9 ), while the a ̂ † 2 scheme is better in the larger amplitude regime. The performance of the two schemes becomes indistinguishable as the amplitude grows sufficiently large.
We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.