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arXiv:2301.02839 · Communications Physics

Method to deterministically generate large-amplitude optical cat states

Zheng-Hong Li, Fei Yu, Zhen-Ya Li, M. Al-Amri, Muhammad Suhail Zubairy

Published Apr 26, 2024• 13 citations
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Abstract

Abstract Cat states, as an important resource in the study of macroscopic quantum superposition and quantum information applications, have garnered widespread attention. To date, preparing large-sized optical cat states has remained challenging. We demonstrate that, by utilizing interaction-free measurement and the quantum Zeno effect, even a fragile quantum microscopic system can deterministically control and become entangled with strong light fields, thereby generating large-amplitude optical cat states. During the entire preparation process, our method ensures that the microscopic system functions within a weak field environment, so that its quantum property can be protected. Furthermore, we show that the preparation of cat states is possible even when the quantum microsystem suffers from significant photon loss, provided that optical losses from classical devices are kept low, which implies that the fidelity of the cat state can be enhanced by improvements to and the perfection of the classical optical system.

DOI
10.1038/s42005-024-01617-6

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Abstract Cat states, as an important resource in the study of macroscopic quantum superposition and quantum information applications, have garnered widespread attention. To date, preparing large-sized optical cat states has remained challenging. We demonstrate that, by utilizing interaction-free measurement and the quantum Zeno effect, even a fragile quantum microscopic system can deterministically control and become entangled with strong light fields, thereby generating large-amplitude optical cat states. During the entire preparation process, our method ensures that the microscopic system functions within a weak field environment, so that its quantum property can be protected. Furthermore, we show that the preparation of cat states is possible even when the quantum microsystem suffers from significant photon loss, provided that optical losses from classical devices are kept low, which implies that the fidelity of the cat state can be enhanced by improvements to and the perfection of the classical optical system.
In 1935, Erwin Schrödinger put forward his famous gedanken experiment in which a microscopic degree of freedom - the emission state of a radioactive atom - and a macroscopic, classical state - the life or death of a cat - are entangled [1]. The resulting state is dubbed a Schrodinger-cat state. According to quantum theory, a measurement of the atom in a superposition basis projects the cat into a macroscopic superposition of being alive and dead. Here, we use coherent laser fields with different optical phases as a macroscopic model system and generate entangled Schrodinger-cat states in a deterministic way [3]. We reflect the coherent pulses from an optical cavity that contains a single strongly-coupled atom. This entangles the spin of the atom with the optical phase of the light field [2]. By manipulating and detecting the atomic state, we create a plethora of flying optical coherent-state superpositions. We reconstruct the corresponding Wigner functions (see Fig. 1) to demonstrate the tunability and non-classicality of the produced light state.
Large-size cat states are especially meaningful and fundamental for exploring the quantum-to-classical transition, as well as promising resources for quantum metrology and fault-tolerant quantum computation. However, amplifying the magnitude of cat states remains challenging because of the growing fragility under decoherence. We propose to generate large cat states by using the dynamical invariant of hybrid qubit-bosonic systems under Hermitian or non-Hermitian time-dependent Hamiltonian. It is a study with the universal quantum control (UQC) theory, in which the system dynamics is analyzed in the ancillary picture via a unitary transformation conditional on the qubit state. The controllable dynamics that can be encoded in the evolution of the dynamical invariant is presented by the Heisenberg equation, which imposes constrains on the Hamiltonian. When the qubit is prepared in a balanced superposed state, the bosonic mode can evolve deterministically from the vacuum state to the cat state of a mean photon number over 120120120. In the Hermitian case, the generation is perfect; and in the non-Hermitian case, the fidelity is over 0.9620.9620.962. Our protocol can also be applied to the generation of the intrinsic cat states and the four-component cat states of large size. Through the preparation of macroscopic quantum states, our work essentially advances UQC to hybrid discrete-continuous variable systems.
We present novel theory of effective realization of large-size optical Schrödinger cat states, which play an important role for quantum communication and quantum computation in the optical domain using laser sources. The treatment is based on the α-representation in infinite Hilbert space which is the decomposition of an arbitrary quantum state in terms of displaced number states characterized by the displacement amplitude α. We find analytical form of the α-representation for both even and odd Schrödinger cat states which is essential for their generation schemes. Two schemes are proposed for generating even/odd Schrödinger cat states of large size |β| (|β| ≥ 2) with high fidelity F (F ≈ 0.99). One scheme relies on an initially offline prepared two-mode entangled state with a fixed total photon number, while the other scheme uses separable photon Fock states as the input. In both schemes, generation of the desired states is heralded by the corresponding measurement outcomes. Conditions for obtaining states useful for quantum information processing are established and success probabilities for their generation are evaluated.
The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.
Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.
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.