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arXiv:1904.05598 · Quantum Science and Technology

Optimal superadiabatic population transfer and gates by dynamical phase corrections

Antti P. Vepsäläinen, S Danilin, Gheorghe Sorin Paraoanu

Published Jan 9, 2018• 37 citations
arXivHTMLPDF

Abstract

Abstract In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.

DOI
10.1088/2058-9565/aaa640

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Abstract In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.
Adiabatic manipulation of the quantum state is an essential tool in modern quantum information processing. Here, we demonstrate the speedup of the adiabatic population transfer in a three-level superconducting transmon circuit by suppressing the spurious nonadiabatic excitations with an additional two-photon microwave pulse. We apply this superadiabatic method to the stimulated Raman adiabatic passage, realizing fast and robust population transfer from the ground state to the second excited state of the quantum circuit.
Reaching a given target quantum state with high fidelity and fast operation speed close to the quantum limit represents an important goal in quantum information science. Here we experimentally demonstrate superadiabatic quantum driving to achieve population transfer in a three-level solid-state spin system at ambient conditions. Starting from traditional stimulated Raman adiabatic passage (STIRAP), our approach implements superadiabatic corrections to the STIRAP Hamiltonian with several pulse shapes, including the paradigmatic Gaussian shapes and trigonometric pulse shapes that guarantee an operation speed equal to the quantum limit. It requires no intense microwave pulses or long transfer times and shows an enhanced robustness against pulse imperfections. Thereby, these results might provide a useful tool for quantum information processing and the coherent manipulation of quantum systems.
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
The superadiabatic quantum driving, producing a perfect adiabatic transfer on a given Hamitonian by introducing an additional Hamiltonian, is theoretically analysed for transfers within a three-level system. Our starting point is the stimulated Raman adiabatic passage, realized through different schemes of laser pulses. We determine the superadiabatic correction for each scheme. The fidelity, robustness and transfer time of all the superadiabatic transfer schemes are discussed. We derive that all superadiabatic corrections are based on a πππ- (or near-πππ)-area pulse coupling between the initial and final states. The benefits in the protocol robustness overcome the difficulties associated to the actual implementation of the three-level superadiabatic transfer.
The stimulated Raman adiabatic passage (STIRAP) allows selective, coherent population transfer in a three-level quantum system by the adiabatic control of two suitably chosen envelopes and delayed laser pulses. However, the long operation time involved with the adiabatic protocols makes them more susceptible to decay and decoherence. A shortcut-to-adiabaticity technique, namely, counterdiabatic driving (CD), suppresses the decoherence-induced loss by speeding up the STIRAP process, thereby enhancing the efficiency and fidelity of population transfer. The superadiabatic STIRAP (saSTIRAP) method requires the application of a shortcut drive or CD pulse, which couples the coherently trapped states in a three-level quantum system. Hence, the closed-loop $\mathrm{\ensuremath{\Lambda}}$ system consisting of all electric dipole-allowed transitions is an essential requirement for saSTIRAP, which is rarely admissible in a natural atom. This paper theoretically investigates an experimentally feasible model for implementing saSTIRAP using a closed-loop $\mathrm{\ensuremath{\Lambda}}$ system with doubly dressed polariton states in a driven circuit QED system. We show a population transfer with efficiencies close to 80.7580.75%80.75 and 98.1098.10%98.10 with fidelities of 89.8689.86%89.86 and 99.0499.04%99.04 for the resonant STIRAP and saSTIRAP protocols, respectively, with experimentally feasible parameters. The efficiency of the population transfer can be further increased by improving the coherence times of the cavity and the transmon qubit. This work may be useful in designing fast, efficient quantum gates for applications in quantum technologies.
Stimulated Raman adiabatic passage is a prominent and widely applied technique that transfers population between quantum states in three-level quantum systems. In this paper, we propose an optimized version of stimulated Raman adiabatic passage, which can be implemented faster than the conventional version. In order to achieve quantum adiabaticity in shorter times, we use the geometric optimization method based on the dynamical quantum geometric tensor to regularize nonadiabatic transitions and to eliminate nonadiabatic effects during the evolution process. Optimal stimulated Raman adiabatic passage can shorten the operation time required for adiabatic population transfer appreciably, thereby avoiding decoherence resulting from long-time evolution. Moreover, optimal stimulated Raman adiabatic passage is robust against systematic and random errors. Our results provide an optimal route for the realization of fast and accurate population transfer in three-level quantum systems.