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Physical Review A

Generation of heralded optical cat states by photon addition

Yi-Ru Chen, Hsien-Yi Hsieh, Jingyu Ning, Hsun-Chung Wu, Hua Li Chen, Zi-Hao Shi, Popo Yang, Ole Steuernagel, Chien-Ming Wu, Ray‐Kuang Lee

Published Aug 1, 2024• 37 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.110.023703

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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×\else\texttimes\fi1052.3\ifmmode\times\else\texttimes\fi{}{10}^{5}2.3\ifmmode×\else\texttimes\fi105 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 ∣\ensuremathα∣\ensuremath≈1.77|\ensuremath{\alpha}|\ensuremath{\approx}1.77∣\ensuremathα∣\ensuremath≈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.
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.
Schrödinger cat states are important non-Gaussian resources for quantum information processing and quantum-enhanced metrology. Although photon subtraction from squeezed vacuum states has proven useful for generating such states in the optical domain, scaling to large amplitudes while maintaining high fidelity and heralding probability remains challenging. To address these obstacles, we analyze alternating squeezing and photon-number-subtraction operations. Rather than optimizing for a single heralding outcome, we formulate cat-state generation as a fidelity-constrained multibranch problem, jointly optimizing the total probability of all photon-number outcomes satisfying a prescribed fidelity threshold at one common experimental setting. Already for plain photon subtraction, this provides a more operational measure of the usable generation probability and can favor parameter configurations that differ from single-branch optima. Considering experimental constraints on available squeezing and photon-number-resolving capability, we demonstrate improvements in fidelity and success probability compared with plain photon subtraction, without necessarily increasing the required squeezing resources. Without restrictions on photon-number resolution, we find that the optimal architecture of the alternating scheme reduces to one of two single-subtraction endpoint configurations, depending on the available squeezing resources. When photon-number resolution is additionally limited, genuinely alternating branches can become advantageous. We derive analytical expressions for the conditional states, cat-state fidelities, and heralding probabilities, enabling efficient multibranch optimization and a systematic analysis of resource trade-offs, sensitivity to experimental parameter deviations, and heralding loss. Together, these results identify the architecture best suited to a given resource budget.
While the interface between strong-field physics and quantum optics offers a unique regime for combining extreme nonlinearity with quantum optical resources, its potential for generating non-classical states of light remains largely unexplored. Standard protocols for generating optical Schrödinger cat states, such as photon subtraction from squeezed light, are inherently limited in the achievable macroscopicity of the state and its scalability. In this work, we bridge this gap by demonstrating that above-threshold ionization driven by bright squeezed light provides a strong-field analogue of photon subtraction, where photoelectron detection acts as a high-intensity heralding mechanism, enabling the generation of large amplitude optical Schrödinger cat states. We characterize the resulting non-Gaussian features and show that they can be tuned via the detected photoelectron momentum, and study their robustness against the experimental imperfections arising from finite momentum resolution at the heralding step. Despite the noise, we show that the generated states can be manipulated to violate a Bell inequality, thereby highlighting their potential for foundational and practical applications. Our results establish strong-field processes as a scalable platform for macroscopic quantum state engineering, opening a route to quantum optics in previously inaccessible regimes.
Conditional addition of photons represents a crucial tool for optical quantum state engineering and it forms a fundamental building block of advanced quantum photonic devices. Here we report on experimental implementation of the conditional addition of several photons. We demonstrate the addition of one, two, and three photons to input coherent states with various amplitudes. The resulting highly nonclassical photon-added states are completely characterized with time-domain homodyne tomography, and the nonclassicality of the prepared states is witnessed by the negativity of their Wigner functions. We experimentally demonstrate that the conditional addition of photons realizes approximate noiseless quantum amplification of coherent states with sufficiently large amplitude. We also investigate certification of the stellar rank of the generated multiphoton-added coherent states, which quantifies the non-Gaussian resources required for their preparation. Our results pave the way towards the experimental realization of complex optical quantum operations based on combination of multiple photon additions and subtractions.
The heralded optical parametric amplifier (OPA) has emerged as a promising tool for quantum state engineering. However, its potential has been limited to coherent state inputs. Here, we introduce a generalized heralded OPA protocol that unlocks a vastly expanded class of quantum phenomena by accepting arbitrary non-classical inputs. With a squeezed vacuum input, the setup functions as an integrated two-photon subtractor, deterministically generating high-fidelity, larger-amplitude squeezed Schrödinger cat states -- an operation previously requiring complex, discrete setups. Furthermore, when fed a small-amplitude SC state, the protocol acts as a non-Gaussianity amplifier, distilling it into high-purity approximations of key quantum resources like specific photon-number superpositions. This work transforms the OPA from a specialized source into a versatile and practical platform for advanced quantum state engineering, enabling the generation of a wide array of non-Gaussian states from a single, integrated setup.