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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Measurement-induced amplification of optical cat-like states

Amine Laghaout, Jonas Schou Neergaard-Nielsen, Johannes Rigas, C. Kragh, Anders Tipsmark, Ulrik L. Andersen

Published May 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleoe-iqec.2013.6801670

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We present a scheme for the amplification of Schr\"odinger cat states that collapses two smaller states onto their constructive interference via a homodyne projection. We analyze the performance of the amplification in terms of fidelity and success rate when the input consists of either exact coherent state superpositions or of photon-subtracted squeezed vacua. The impact of imprecise homodyne detection and of impure squeezing is quantified. We also assess the scalability of iterated amplifications.
Iterative CZC_ZCZ​-gate-based protocol for squeezed Schrödinger cat state engineering
Squeezed optical Schrödinger cat states constitute a key resource for both fundamental tests of quantum theory and up-to-date quantum technologies. We propose a measurement-assisted gate for the generation and manipulation of the cat states. In this scheme, an ancilla in the non-Gaussian small-amplitude (in general, squeezed) Schrödinger cat state and the target oscillator initially prepared in a squeezed vacuum (or coherent) state are subjected to a quantum nondemolition (QND) entangling operation followed by projective homodyne measurement. The proposed gate enables generation of high-fidelity squeezed Schrödinger cat states with controllable size and squeezing with tunable fidelity/success-probability trade-off. We also introduce an iterative, homodyne-conditioned CZC_ZCZ​-based protocol for cat-state amplification. The parameter regimes required to achieve the desired fidelity and the success probability are analyzed. The approach is well suited for applications in measurement-based quantum computing and hybrid quantum networks where non-Gaussian resources enhance computational and communication capabilities.
Optical "Schrödinger cat" states, the non-classical superposition of two quasi-classical coherent states, serve as a basis for gedanken experiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical "Schrödinger cats" by adding a photon to a squeezed vacuum state, so far only photon-subtraction protocols have been realized. Photon-addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate "Schrödinger cats" at rates exceeding 8.5×1048.5 \times 10^48.5×104 counts per second; at least one order of magnitude higher than all previously reported realizations. Wigner distributions with pronounced negative parts are demonstrated at down to -8.89 dB squeezing, even when the initial squeezed vacuum input state has low purity. Benchmarking against such a degraded squeezed input state we report a maximum fidelity of more than 80% with a maximum cat amplitude of ∣α∣≈1.66|α| \approx 1.66∣α∣≈1.66. Our experiment uses photon-addition from pairs, one of those photons is used for monitoring, giving us enhanced control; moreover the pair production rates are high and should allow for repeated application of photon-addition via repeat-stages.
Optical cat states, the nonclassical superposition of two quasi-classical coherent states, serve as a basis for gedankenexperiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical cat states by adding a photon to a squeezed vacuum state; so far only photon-subtraction protocols have been realized. Photon addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate cat states at rates exceeding $2.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ counts per second. Our most highly squeezed vacuum input state shows \ensuremath{-}8.9 dB squeezing, but such squeezing entails some degradation---in this case, 15.1 dB antisqueezing. Even so, our approach enables us to synthesize a state with a maximum cat amplitude of $|\ensuremath{\alpha}|\ensuremath{\approx}1.77$ whose Wigner distribution still shows pronounced negative parts. Our experimental implementation with controlled photon addition demonstrates a powerful and robust building block for advanced quantum state engineering and shows that heralded photon addition can be controlled well and performed at high rates.
We proposed and analyzed a scheme to generate large-size Schr\"odinger cat states based on linear operations of Fock states, squeezed vacuum states, and conditional measurements. By conducting conditional measurements via photon number detectors, two unbalanced small-amplitude Schr\"odinger kitten states combined by a beam splitter can be amplified to a large-size cat state with the same parity. According to simulation results, two Schr\"odinger odd kitten states with amplitudes of $|\ensuremath{\beta}|=1.06$ and $|\ensuremath{\beta}|=1.11$ generated from one-photon-subtracted 3 dB squeezed vacuum states, are amplified to an odd cat state of $|\ensuremath{\beta}|=1.73$ with a fidelity of F=99F=99%F=99. A large-size Schr\"odinger odd cat state with $|\ensuremath{\beta}|=2.51$ and F=97.30F=97.30%F=97.30 is predicted when 5.91 dB squeezed vacuum states are employed. According to the analysis on the impacts of experimental imperfections in practice, Schr\"odinger odd cat states of $|\ensuremath{\beta}|>2$ are available. A feasible configuration based on a quantum frequency comb is developed to realize the large-size cat state generation scheme we proposed.
The optical Schrödinger’s cat is highly anticipated for its potential to realize fault-tolerant quantum computing and quantum metrology. To attain a good performance in these processes, the amplitude of cat states is desired to be as high as possible. Here, we demonstrate the enlargement of a cat state through the superposition of two kitten states in coupled waveguides. Under reasonable superposition coefficients, the interference between two nearby coherent state components in the initial kittens will produce a coherent-like state with a larger amplitude, enabling the creation of larger cat-like states. Based on the above mechanism, we theoretically demonstrate the superposition of two kittens in coupled waveguides through conditional measurements. In an appropriate propagation length, a cat state, whose amplitude is enlarged beyond α 0 2 + β 0 2 , is achieved with high fidelity and a high success probability when the amplitudes of input kittens are α 0 and i β 0 , respectively. The mechanism we propose has the potential to be realized in other systems, and it could be extended to amplify other macroscopic quantum states. The physical realization based on coupled waveguides demonstrates the ability to efficiently amplify cat states and is expected to become a competitive approach for on-chip cat state preparation.