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arXiv:1801.06362 · Physical Review A

Faithful state transfer between two-level systems via an actively cooled finite-temperature cavity

L. Sárkány, József Fortágh, David Petrosyan

Published Mar 28, 2018• 19 citations
arXivHTMLPDF

Abstract

We consider state transfer between two qubits---effective two-level systems represented by Rydberg atoms---via a common mode of a microwave cavity at finite temperature. We find that when both qubits have the same coupling strength to the cavity field, at large enough detuning from the cavity mode frequency, quantum interference between the transition paths makes the swap of the excitation between the qubits largely insensitive to the number of thermal photons in the cavity. When, however, the coupling strengths are different, the photon-number-dependent differential Stark shift of the transition frequencies precludes efficient transfer. Nevertheless, using an auxiliary cooling system to continuously extract the cavity photons, we can still achieve a high-fidelity state transfer between the qubits.

DOI
10.1103/physreva.97.032341

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We consider state transfer between two qubits---effective two-level systems represented by Rydberg atoms---via a common mode of a microwave cavity at finite temperature. We find that when both qubits have the same coupling strength to the cavity field, at large enough detuning from the cavity mode frequency, quantum interference between the transition paths makes the swap of the excitation between the qubits largely insensitive to the number of thermal photons in the cavity. When, however, the coupling strengths are different, the photon-number-dependent differential Stark shift of the transition frequencies precludes efficient transfer. Nevertheless, using an auxiliary cooling system to continuously extract the cavity photons, we can still achieve a high-fidelity state transfer between the qubits.
For a standard two-level atom coupled to the quantized field of a resonant cavity, finite-temperature effects lead to thermal occupation of the cavity modes that obfuscates measurement of the quantum nature of the atom-light interaction. In this paper we demonstrate that using a hybrid system of a superconducting cavity coupled to a multilevel Rydberg atom, it is possible to observe the quantum nature of strong coupling even at finite temperatures and to exploit this coupling to permit cooling of the thermal microwave mode towards the ground state, enabling observation of coherent vacuum Rabi oscillations even at 4 K for realistic experimental parameters. Cooling for multiple atoms is also explored, showing maximal cooling for small samples, making this a viable approach to cavity cooling with potential applications in long-range coupling of superconducting qubits via thermal waveguides.
We propose an implementation of a universal quantum gate between pairs of spatially separated atoms in a microwave cavity at finite temperature. The gate results from reversible laser excitation of Rydberg states of atoms interacting with each other via exchange of virtual photons through a common cavity mode. Quantum interference of different transition paths between the two-atom ground and double-excited Rydberg states makes both the transition amplitude and resonance largely insensitive to the excitations in the microwave cavity quantum bus which can therefore be in any superposition or mixture of photon number states. Our scheme for attaining ultra-long-range interactions and entanglement also applies to mesoscopic atomic ensembles in the Rydberg blockade regime and is scalable to many ensembles trapped within a centimeter-sized microwave resonator.
We study the entanglement properties of two three-level Rydberg atoms passing through a single-mode cavity. The interaction of an atom with the cavity field allows the atom to make a transition from the uppermost (lowermost) to the lowermost (uppermost) level by emission (absorption) of two photons via the middle level. We employ an effective Hamiltonian that describes the system with a Stark-shifted two-photon atomic transition. We compute the entanglement of formation of the joint two-atom state as a function of Rabi angle gt . It is shown that the Stark shift can be used to enhance the magnitude of atomic entanglement over that obtained in the resonant condition for certain parameter values. We find that though the two-atom entanglement generally diminishes with the increase of the two-photon detuning and the Stark shift, it is possible to sustain the entanglement over a range of interaction times by making the detuning and the Stark shift compensate each other. Similar characteristics are also obtained for a thermal state cavity field.
We study the entanglement properties of two three-level Rydberg atoms passing through a single-mode cavity. The interaction of an atom with the cavity field allows the atom to make a transition from the upper most (lower most) to the lower most (upper most) level by emission (absoprtion) of two photons via the middle level. We employ an effective Hamiltonian that describes the system with a Stark shifted two-photon atomic transition. We compute the entanglement of formation of the joint two-atom state as a function of Rabi angle gtgtgt. It is shown that the Stark shift can be used to enhance the magnitude of atomic entanglement over that obtained in the resonant condition for certain parameter values. We find that though the two-atom entanglement generally diminishes with the increase of the two-photon detuning and the Stark shift, it is possible to sustain the entanglement over a range of interaction times by making the detuning and the Stark shift compensate each other. Similar characteristics are obtained for a thermal state cavity field too.
We study the nonlinear dynamics of an ensemble of cold trapped atoms with a hyperfine transition magnetically coupled to a resonant microwave cavity mode. Despite the minute single-atom coupling, one obtains strong coupling between collective hyperfine qubits and microwave photons, enabling coherent transfer of an excitation between the long-lived atomic qubit state and the mode. Evidence of strong coupling can be obtained from the cavity transmission spectrum even at finite thermal photon number. The system makes it possible to study further prominent collective phenomena such as superradiant decay of an inverted ensemble or the building of a narrowband stripline micromaser locked to an atomic hyperfine transition.
We develop a theoretical framework for cooling a microwave cavity mode using a Poisson stream of internally correlated pairs of two-level systems and analyze its performance under realistic dissipation. Starting from a Lindblad model of a phonon-tethered cavity interacting with sequentially injected atom pairs, we derive closed-form expressions for the steady-state cavity occupation and effective temperature. Two coupling geometries are examined: a one-atom configuration, where only one member of each pair interacts with the cavity, and a two-atom configuration, where both atoms couple collectively. The single-atom model enables cooling below the phonon bath but not below the reservoir temperature, whereas the two-atom scheme exhibits enhanced refrigeration - pair correlations modify the cavity's upward and downward transition rates so that the steady-state temperature can fall well below that of the reservoir for weak phonon damping. We map the parameter space including detuning, coupling strength, damping, and intra-pair exchange, identifying cooling valleys near resonance and the crossover between reservoir- and phonon-dominated regimes. The two-atom configuration thus realizes a genuine quantum-enhanced cooling mechanism absent in the single-atom case. We further outline an experimental implementation using two superconducting qubits repeatedly prepared, coupled, and reset inside a 3D cavity. Realistic reset and flux-tuning protocols support MHz-rate interaction cycles, enabling engineered reservoirs to impose cavity temperatures of 50-120 mK even when the cryostat is at ~1 K, offering a pathway to autonomous, on-chip refrigeration of microwave modes in scalable quantum hardware.