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arXiv:1708.04042 · Optics Express

Generation of highly pure Schrödinger’s cat states and real-time quadrature measurements via optical filtering

Warit Asavanant, Kota Nakashima, Yu Shiozawa, Jun-Ichi Yoshikawa, Akira Furusawa

Published Dec 11, 2017• 62 citations
arXivHTMLPDF

Abstract

Until now, Schrödinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schrödinger's cat state with the value of $-0.184$ at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The temporal mode also becomes exponentially rising in our method, which allows us to make a real-time quadrature measurement on Schrödinger's cat states, and we obtained the value of $-0.162$ at the origin of the Wigner function.

DOI
10.1364/oe.25.032227

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Until now, Schrödinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schrödinger's cat state with the value of −0.184-0.184−0.184 at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The temporal mode also becomes exponentially rising in our method, which allows us to make a real-time quadrature measurement on Schrödinger's cat states, and we obtained the value of −0.162-0.162−0.162 at the origin of the Wigner function.
We have generated and measured an approximation of an optical Schrödinger cat state by photon subtraction from a squeezed state. Using single-photon avalanche photodiode detectors and photon-number-resolving transition edge sensors, we were able to extract Wigner distributions for one or two photons subtracted from the squeezed state, resulting in both an odd and even cat state. The one-photon-subtracted Wigner distribution shows measured negative features (without any correction), indicating quantum character. The Wigner distribution of the two-photon-subtracted state is negative after correcting for homodyne losses. A full statistical analysis is under way to quantify the magnitude and fidelity of the cat states generated.
We propose a high-rate generation method of optical Schrödinger cat states [1] . More than a decade, the standard method of cat-state generation has been photon subtraction from squeezed vacuum states [2] . Its constraints on experimental parameters, however, limit the generation rate. We overcome the problem by considering photon-number measurement in one mode of arbitrary two-mode Gaussian states, which we call "generalized photon subtraction". Analysis of such a general situation is challenging, but we analytically derive an efficient condition by describing the state-generation process using wave functions. Supposing realistic experimental conditions, the generation rate of cat states with large-amplitude (| α| ≥ 2) is improved by multiple orders from the conventional photon subtraction. Our proposal would open a way for quantum error correction and coherent-state-based quantum computing.
We propose a high-rate generation method of optical Schr\"odinger cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\ensuremath{\alpha}|\ensuremath{\ge}2)$ can exceed megacounts per second, about 103{10}^{3}103 to 106{10}^{6}106 times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. The ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalability has been demonstrated but preparation of non-Gaussian states of light remains as a challenging task for universality and fault tolerance. Our proposal reduces the difficulty of the state preparation and opens a way for practical applications in quantum optics.
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.
Non-Gaussian states are essential resources for universal, fault-tolerant optical quantum computing, but their generation rate remains limited by low heralding probabilities and operation in nanosecond temporal modes. Here, we demonstrate multi-photon generalized photon subtraction in picosecond optical wave packets, establishing the state-generation capability required for high-rate operation by addressing the temporal-mode bottleneck that has constrained the achievable rate. Two interfering ultrashort squeezed vacua are heralded by photon-number-resolving detection with a high-speed transition-edge sensor and characterized by pulsed homodyne detection matched to 10-ps temporal modes at a 5-MHz pump repetition rate. We reconstruct Wigner functions without loss correction that exhibit up to four distinct negative regions for four-photon heralding, together with an effective cat-state amplitude of αeff=1.69α_{\mathrm{eff}} = 1.69αeff​=1.69. This amplitude approaches the range of practical relevance for fault-tolerant cat-code architectures and for adaptive breeding toward logical-qubit generation, while the picosecond temporal mode establishes a platform compatible with high-rate, scalable time-multiplexed photonic architectures.