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arXiv:1711.03821 · Physical Review A

Progress towards macroscopic spin and mechanical superposition via Rydberg interaction

Mohammadsadegh Khazali

Published Oct 18, 2018• 21 citations
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Abstract

This paper is a proposal for the generation of a many-body entangled state in atomic and mechanical systems. Here the detailed feasibility study shows that application of a strong Rydberg dressing interaction and a fast bifurcation scheme in a Bose-Einstein condensate of Rb atoms, results in the formation of large cat states. By detailed study of the decoherence effects using the quantum jump Monte Carlo approach and taking into account the obstacles like collective decoherence and level mixing, this proposal predicts the formation of a 700-atom cat state. Subsequent transfer of the generated superposition to far separated mechanical oscillators is proposed, using dipole coupling between Rydberg atoms and charged cantilevers.

DOI
10.1103/physreva.98.043836

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This paper is a proposal for the generation of a many-body entangled state in atomic and mechanical systems. Here the detailed feasibility study shows that application of a strong Rydberg dressing interaction and a fast bifurcation scheme in a Bose-Einstein condensate of Rb atoms, results in the formation of large cat states. By detailed study of the decoherence effects using the quantum jump Monte Carlo approach and taking into account the obstacles like collective decoherence and level mixing, this proposal predicts the formation of a 700-atom cat state. Subsequent transfer of the generated superposition to far separated mechanical oscillators is proposed, using dipole coupling between Rydberg atoms and charged cantilevers.
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.
The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose–Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure two-body interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas–Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results and point out possible solutions for future approaches. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.
We explore the possibility of engineering quantum states of a charged mechanical oscillator by coupling it to a stream of atoms in superpositions of high-lying Rydberg states. Our scheme relies on the driving of a two-phonon resonance within the oscillator by coupling it to an atomic two-photon transition. This approach effectuates a controllable open system dynamics on the oscillator that in principle permits versatile dissipative creation of squeezed and other nonclassical states which are central to sensing applications or for studies of fundamental questions concerning the boundary between classical and quantum-mechanical descriptions of macroscopic objects. We show that these features survive thermal coupling of the oscillator with the environment. We perform a detailed feasibility study finding that current state-of-the-art parameters result in atom-oscillator couplings which are too weak to efficiently implement the proposed oscillator state preparation protocol. Finally, we comment on ways to circumvent the present limitations.
Due to their coherence properties, dilute atomic gas Bose-Einstein condensates seem a versatile platform for controlled creation of mesoscopically entangled states with a large number of particles and allow controlled studies of their decoherence. However, the creation of such states intrinsically involves many-body quantum dynamics that cannot be captured by mean-field theory and, thus, invalidates the most common methods for the description of condensates. We follow up on a proposal in which a condensate cloud as a whole is brought into a superposition of two different spatial locations by mapping entanglement from a strongly interacting Rydberg atomic system onto the condensate using off-resonant laser dressing [Phys. Rev. Lett. 115 040401 (2015)]. A variational many-body ansatz akin to recently developed multiconfigurational methods allows us to model this entanglement mapping step explicitly, while still preserving the simplicity of mean-field physics for the description of each branch of the superposition. In the second part of the article, we model the decoherence process due to atom losses in detail. Altogether we confirm earlier estimates that tightly localized clouds of 400 atoms can be brought into a quantum superposition of two locations about $3\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ apart and remain coherent for about 1 ms.
We theoretically investigate the effect of multimode dynamics on the creation of macroscopic superposition states (spin-cat states) in Bose-Einstein condensates via one-axis twisting. A two-component Bose-Einstein condensate naturally realizes an effective one-axis twisting interaction, under which an initially separable state will evolve toward a spin-cat state. However, the large evolution times necessary to realize these states is beyond the scope of current experiments. This evolution time is proportional to the degree of asymmetry in the relative scattering lengths of the system, which results in the following trade-off: faster evolution times are associated with an increase in multimode dynamics, and we find that generally multimode dynamics reduce the degree of entanglement present in the final state. However, we find that highly entangled catlike states are still possible in the presence of significant multimode dynamics and that these dynamics impose a speed limit on the evolution of such states.
We propose to create superposition states of over 100 strontium atoms in a ground state or metastable optical clock state using the Kerr-type interaction due to Rydberg state dressing in an optical lattice. The two components of the superposition can differ by an order of 300 eV in energy, allowing tests of energy decoherence models with greatly improved sensitivity. We take into account the effects of higher-order nonlinearities, spatial inhomogeneity of the interaction, decay from the Rydberg state, collective many-body decoherence, atomic motion, molecular formation, and diminishing Rydberg level separation for increasing principal number.