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arXiv:2312.05218

Fast and robust cat state preparation utilizing higher order nonlinearities in Rydberg ensembles

S. P. Zhao, Matthias G. Krauss, Tom Bienaimé, S. Whitlock, Christiane P. Koch, Sofia Qvarfort, A. Metelmann

Published Dec 8, 2023• 0 citations
arXivHTMLPDF

Abstract

In optical and solid-state architectures, low-order nonlinearities are commonly exploited for quantum state preparation due to their practical accessibility and controllability, while higher-order contributions are typically much weaker and treated as unwanted perturbations. Here, we alternatively show that detuned Rydberg ensembles provide a natural platform where higher-order Kerr nonlinearities can become comparable in strength to lower-orders near multiphoton resonances. We demonstrate that these nonlinearities can be harnessed as a resource for the rapid preparation of non-Gaussian states, with the coexistence of multiple Kerr orders substantially accelerating the evolution of an initial coherent state into Schrödinger cat states. Furthermore, by combining the nonlinear dynamics with a controllable linear drive, we can gain the full control over the evolution trajectory, thereby achieving cat-state generation directly from vacuum on timescales beyond the genuine Kerr evolution. Our results establish a paradigm in which naturally occurring higher-order nonlinearities are transformed from unwanted imperfections into a valuable resource for quantum state engineering.

DOI
10.48550/arxiv.2312.05218

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In optical and solid-state architectures, low-order nonlinearities are commonly exploited for quantum state preparation due to their practical accessibility and controllability, while higher-order contributions are typically much weaker and treated as unwanted perturbations. Here, we alternatively show that detuned Rydberg ensembles provide a natural platform where higher-order Kerr nonlinearities can become comparable in strength to lower-orders near multiphoton resonances. We demonstrate that these nonlinearities can be harnessed as a resource for the rapid preparation of non-Gaussian states, with the coexistence of multiple Kerr orders substantially accelerating the evolution of an initial coherent state into Schrödinger cat states. Furthermore, by combining the nonlinear dynamics with a controllable linear drive, we can gain the full control over the evolution trajectory, thereby achieving cat-state generation directly from vacuum on timescales beyond the genuine Kerr evolution. Our results establish a paradigm in which naturally occurring higher-order nonlinearities are transformed from unwanted imperfections into a valuable resource for quantum state engineering.
Cat states are maximally entangled states with applications in metrology and fault-tolerant quantum computation. Experiments have revealed that Rydberg collective avalanche decoherence acts as a bottleneck for cat creation with Rydberg atoms. This process initiates after the blackbody-radiation-induced decay of Rydberg atoms and sets a strong limit on the cat creation time. These findings necessitate the exploration of new ideas to accelerate current Rydberg cat schemes. To enhance the interaction-to-loss ratio, this paper delves into cat-state formation in the strong-Rydberg-dressing regime, uncovering the emergence of cat states despite the presence of complex orders of nonlinearities. This unexplored regime demonstrates the potential for rapid cat-state formation, which is particularly beneficial for operation in typical two-dimensional lattices in Rydberg laboratories. In an extreme case, this paper demonstrates that second-order nonlinearity could be isolated under resonant Rydberg driving if a large number of atoms are accommodated inside the blockade volume. The resonant model significantly enhances the interaction-to-loss ratio while circumventing the adiabaticity condition, allowing fast switching of lasers. In addition, this paper presents a method for generating multicomponent cat states, which are superpositions of mmm coherent spin states ($|m\text{\ensuremath{-}}\text{CSS}\ensuremath{\rangle}$). The maximum value of mmm is determined by the number of atoms within the blockade radius, where m=Nm=\sqrt{N}m=N​. The states with larger mmm are more robust against the presence of multiple orders of nonlinearity in the strong-dressing Hamiltonian and are accessible in a much shorter time compared to traditional two-component cat states.
Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally present in this kind of system. We perform detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits generation of all other complex non-Gaussian states with negative Wigner functions resulting from Kerr nonlinear interaction. Especially, superpositions of several coherent states are achieved at a fraction of the time necessary to produce the cat state.
Abstract Macroscopic cat states have been widely studied to illustrate fundamental principles of quantum physics as well as their applications in quantum information processing. In this paper, we propose a quantum speed-up method for the creation of cat states in a Kerr nonlinear resonator (KNR) via optimal adiabatic control. By simultaneously adiabatic tuning the cavity-field detuning and driving field strength, the width of the minimum energy gap between the target trajectory and non-adiabatic trajectory can be widened, which allows us to accelerate the evolution along the adiabatic path. Compared with the previous proposal, preparing cat states only by controlling two-photon pumping strength, our method can prepare the target state with a shorter time, a high-fidelity and a large non-classical volume. It is worth noting that the cat state prepared here is also robust against single-photon loss. Moreover, when we consider the KNR with a large initial detuning, our proposal will create a large-size cat state successfully. This proposal for preparing cat states can be implemented in superconducting quantum circuits, which provides a quantum state resource for quantum information encoding and fault-tolerant quantum computing.
Schrödinger cat states - quantum superpositions of classically or macroscopically distinct states - constitute a powerful resource for quantum computing, enhanced metrology, and probing coherence on large scales. Encoding such states in the phase space of an oscillator requires a nonlinearity, typically inherited from an auxiliary degree of freedom such as atomic spin or a Josephson junction. Neutral atoms trapped in reconfigurable optical tweezer arrays - a leading platform for quantum science and computing - provide an intrinsic nonlinearity via the motion of a single atom in a tightly focused trap. However, this self-Kerr mechanism has not previously been exploited for cat-state generation, and remains largely unexplored as a resource for motional-state control. Here we realize Schrödinger cat states in the quantized motion of a single neutral atom trapped in an optical tweezer. By modulating the depth and position, we demonstrate parity control of both Kerr-cat and Fock states alongside tunable nonlinearity, establishing a spin- and species-independent framework for controlling motion. We further show that the cat-state encoding is intrinsically robust against trap-frequency fluctuations that otherwise limit the fidelity of direct Fock-state transitions. These results establish Kerr-based control of neutral-atom motion as a new paradigm for cat-state and bosonic-state engineering in optical tweezers, providing a route toward quantum-error-correcting codes such as grid states, and toward quantum-enhanced sensing with arrays of non-Gaussian states.
Non-Gaussian quantum states have been deterministically prepared and autonomously stabilized in single-and two-mode circuit quantum electrodynamics architectures via engineered dissipation.However, it is currently unknown how to scale up this technique to multimode non-Gaussian systems.Here, we upgrade dissipation engineering to collective (normal) modes of nonlinear resonator arrays and show how to stabilize multimode Schrödinger cat states.These states are multiphoton and multimode quantum superpositions of coherent states in a single normal mode delocalized over an arbitrary number of cavities.We consider tailored dissipative coupling between resonators that are parametrically driven and feature an on-site nonlinearity, which is either a Kerr-type nonlinearity or an engineered two-photon loss.For both types of nonlinearity, we find the same exact closed-form solutions for the two-dimensional steady-state manifold spanned by superpositions of multimode Schrödinger cat states.We further show that, in the Zeno limit of strong dissipative coupling, the even-parity multimode cat state can be deterministically prepared from the vacuum.Remarkably, engineered two-photon loss gives rise to a fast relaxation toward the steady state, protecting the state preparation against decoherence due to intrinsic single-photon losses and imperfections in tailored dissipative coupling, which sets in at longer times.The relaxation time is independent of system size making the state preparation scalable.Multimode cat states are naturally endowed with a noise bias that increases exponentially with system size and can thus be exploited for enhanced robust encoding of quantum information.
We propose a scheme to generate spin cat states, i.e., superpositions of maximally separated quasiclassical states on a single high-dimensional nuclear spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to drive the nucleus significantly faster than usual gate sequences, achieving collapses and revivals two orders of magnitude faster than the dephasing timescale. Furthermore, these states are engineered without entanglement with an ancilla, hence, are robust against error propagation. With our multitone control, we can realize arbitrary high-spin rotations within an experimentally feasible regime, as well as transform a spin coherent state to a spin cat state using only phase modulation, opening the possibility of storing and manipulating high-fidelity cat states. Published by the American Physical Society 2024