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arXiv:1305.0204 · Physical Review B

Design of a Lambda system for population transfer in superconducting nanocircuits

G. Falci, Angelo La Cognata, Marco Berritta, Antonio D’Arrigo, Elisabetta Paladino, Bernardo Spagnolo

Published Jun 20, 2013• 93 citations

Abstract

The implementation of a Lambda scheme in superconducting artificial atoms could allow detection of stimulated Raman adiabatic passage (STIRAP) and other quantum manipulations in the microwave regime. However, symmetries which on one hand protect the system against decoherence yield selection rules which may cancel coupling to the pump external drive. The tradeoff between efficient coupling and decoherence due to broad-band colored noise (BBCN), which is often the main source of decoherence, is addressed in the class of nanodevices based on the Cooper pair box (CPB) design. We study transfer efficiency by STIRAP, showing that substantial efficiency is achieved for off-symmetric bias only in the charge-phase regime. We find a number of results uniquely due to non-Markovianity of BBCN, namely (a) the efficiency for STIRAP depends essentially on noise channels in the trapped subspace; (b) low-frequency fluctuations can be analyzed and represented as fictitious correlated fluctuations of the detunings of the external drives; and (c) a simple figure of merit for design and operating prescriptions allowing the observation of STIRAP is proposed. The emerging physical picture also applies to other classes of coherent nanodevices subject to BBCN.

DOI: 10.1103/physrevb.87.214515

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The implementation of a Lambda scheme in superconducting artificial atoms could allow detection of stimulated Raman adiabatic passage (STIRAP) and other quantum manipulations in the microwave regime. However, symmetries which on one hand protect the system against decoherence yield selection rules which may cancel coupling to the pump external drive. The tradeoff between efficient coupling and decoherence due to broad-band colored noise (BBCN), which is often the main source of decoherence, is addressed in the class of nanodevices based on the Cooper pair box (CPB) design. We study transfer efficiency by STIRAP, showing that substantial efficiency is achieved for off-symmetric bias only in the charge-phase regime. We find a number of results uniquely due to non-Markovianity of BBCN, namely (a) the efficiency for STIRAP depends essentially on noise channels in the trapped subspace; (b) low-frequency fluctuations can be analyzed and represented as fictitious correlated fluctuations of the detunings of the external drives; and (c) a simple figure of merit for design and operating prescriptions allowing the observation of STIRAP is proposed. The emerging physical picture also applies to other classes of coherent nanodevices subject to BBCN.

Recent experiments have demonstrated coherent phenomena in three-level systems based on superconducting nanocircuits. This opens the possibility to detect Stimulated Raman Adiabatic Passage (STIRAP) in artificial atoms. Low-fequency noise (often 1/f) is one of the main sources of decoherence in these systems, and we study its effect on the transfer efficiency. We propose a way to analyze low frequency fluctuations in terms of fictitious correlated fluctuations of external parameters. We discuss a specific implementation, namely the Quantronium setup of a Cooper-pair box, showing that optimizing the trade-off between efficient coupling and protection against noise may allow us to observe coherent population transfer in this nanodevice.

The implementation of a three-level Lambda System in artificial atoms would allow to perform advanced control tasks typical of quantum optics in the solid state realm, with photons in the

\mathrm{μm}

/mm range. However hardware constraints put an obstacle since protection from decoherence is often conflicting with efficient coupling to external fields. We address the problem of performing conventional STImulated Raman Adiabatic Passage (STIRAP) in the presence of low-frequency noise. We propose two strategies to defeat decoherence, based on "optimal symmetry breaking" and dynamical decoupling. We suggest how to apply to the different implementations of superconducting artificial atoms, stressing the key role of non-Markovianity.

We propose a protocol for the manipulation of a three-level artificial atom in Lambda ($\mathrm{\ensuremath{\Lambda}}$) configuration. It allows faithful, selective and robust population transfer analogous to stimulated Raman adiabatic passage ($\mathrm{\ensuremath{\Lambda}}$-STIRAP), in last-generation superconducting artificial atoms, where protection from noise implies the absence of a direct pump coupling. It combines the use of a two-photon pump pulse with suitable advanced control, operated by a slow modulation of the phase of the external fields, leveraging on the stability of semiclassical microwave drives. This protocol is a building block for manipulation of microwave photons in complex quantum architectures. Its demonstration would be a benchmark for the implementation of a class of multilevel advanced control procedures for quantum computation and microwave quantum photonics in systems based on artificial atoms.

In this paper we propose a protocol to achieve coherent population transfer between two states in a three-level atom by using two ac fields. It is based on the physics of stimulated Raman adiabatic passage (STIRAP), but it is implemented with the constraint of a reduced control, namely, one of the fields cannot be switched off. A combination of frequency chirps is used with resonant fields, allowing us to achieve approximate destructive interference, despite the fact that an exact dark state does not exist. This chirped STIRAP protocol is tailored for applications to artificial atoms, where architectures with several elementary units can be strongly coupled but where the possibility of switching on and off such couplings is often very limited. Demonstration of this protocol would be a benchmark for the implementation of a class of multilevel advanced control procedures for quantum computation and microwave quantum photonics in artificial atoms.

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

80.75%

and

98.10%

with fidelities of

89.86%

and

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.

The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechanical resonator by vacuum-stimulated adiabatic passage with the superconducting nanocircuit coupled to the resonator.