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Conditional Production of Schroedinger Cat States with Inefficient Photon Detection

Austin P. Lund, Hyunseok Jeong, Timothy C. Ralph, M. S. Kim

Published Dec 31, 2003• 0 citations
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Abstract

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states (Schroedinger's cat state) 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 free propagating optical cat state with a large coherent amplitude ($\\alpha>2$) and high fidelity ($F>0.99$). In contrast to all previous schemes to generate such a state, our scheme does not need photon resolving measurements nor Kerr-type nonlinear interactions.

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It is shown that a linear superposition of two macroscopically distinguishable optical coherent states (Schroedinger's cat state) 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 free propagating optical cat state with a large coherent amplitude (alpha>2\\alpha>2alpha>2) and high fidelity (F>0.99F>0.99F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon resolving measurements nor Kerr-type nonlinear interactions.
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.
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.
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We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It nondeterministically distills coherent-state superpositions (CSS's) with large amplitudes out of CSS's with small amplitudes using inefficient photon detection. The small CSS's required to produce CSS's with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single-photon sources and boosts negativity of Wigner functions of quantum states.
Optical Schrödinger cat states are non-Gaussian states with applications in quantum technologies, such as for building error-correcting states in quantum computing. Yet the efficient generation of high-fidelity optical Schrödinger cat states is an outstanding problem in quantum optics. Here, we propose using squeezed superpositions of zero and two photons, ∣θ⟩=cos⁡(θ/2)∣0⟩+sin⁡(θ/2)∣2⟩|θ\rangle = \cos{(θ/2)}|0\rangle + \sin{(θ/2)}|2\rangle∣θ⟩=cos(θ/2)∣0⟩+sin(θ/2)∣2⟩, as ingredients for protocols to efficiently generate high-fidelity cat states. We present a protocol using linear optics with success probability P≳50%P\gtrsim 50\%P≳50% that can generate cat states of size ∣α∣2=5|α|^2=5∣α∣2=5 with fidelity F>0.99F>0.99F>0.99. The protocol relies only on detecting single photons and is remarkably tolerant of loss, with 2%2\%2% detection loss still achieving F>0.98F>0.98F>0.98 for cats with ∣α∣2=5|α|^2=5∣α∣2=5. We also show that squeezed θθθ states are ideal candidates for nonlinear photon subtraction using a two-level system with near deterministic success probability and fidelity F>0.98F>0.98F>0.98 for cat states of size ∣α∣2=5|α|^2=5∣α∣2=5. Schemes for generating θθθ states using quantum emitters are also presented. Our protocols can be implemented with current state-of-the-art quantum optics experiments.
We propose an optical scheme to generate a superposition of coherent states with enhanced size adopting an interferometric setting at the single-photon level currently available in the laboratory. Our scheme employs a nondegenerate optical parametric amplifier together with two beam splitters so that the detection of single photons at the output conditionally implements the desired superposition of second-order photonic operations. We analyze our proposed scheme by considering realistic on-off photodetectors with nonideal efficiency in heralding the success of conditional events. A high-quality performance of our scheme is demonstrated in view of various criteria such as quantum fidelity, mean output energy, and measure of quantum interference.