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Physical Review B

Suppression of energy-relaxation-induced decoherence in Λ -type three-level SQUID flux qubits: A dark-state approach

Zhongyuan Zhou, Shih‐I Chu, Siyuan Han

Published Sep 23, 2004• 19 citations
Publisher

Abstract

We report a theoretical investigation of decoherence induced by energy relaxation of the auxiliary level in the $\ensuremath{\Lambda}$-type three-level SQUID flux qubits. We show that the energy-relaxation-induced decoherence in this particular case is proportional to the average population of the auxiliary level and thus can be effectively suppressed by the use of a dark-state approach in which the auxiliary level is unpopulated. We demonstrate through bit-flip operation that the dark state can be realized by means of the stimulated Raman adiabatic passage (STIRAP). An extension of the dark-state scheme to create any superposition state is straightforward.

DOI
10.1103/physrevb.70.094513

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We report a theoretical investigation of decoherence induced by energy relaxation of the auxiliary level in the \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type three-level SQUID flux qubits. We show that the energy-relaxation-induced decoherence in this particular case is proportional to the average population of the auxiliary level and thus can be effectively suppressed by the use of a dark-state approach in which the auxiliary level is unpopulated. We demonstrate through bit-flip operation that the dark state can be realized by means of the stimulated Raman adiabatic passage (STIRAP). An extension of the dark-state scheme to create any superposition state is straightforward.
Coherent stimulated Raman adiabatic passages (STIRAP) based on a dark state have many applications in diverse quantum systems. In the case of large single-photon detuning in three-level $\ensuremath{\Lambda}$ systems, one of the bright states almost does not involve the excited state and then acts as the dark state. In this paper, we report the experimental observation of STIRAP based on the dark state, as well as b-STIRAP based on the above bright state, with the same transfer efficiency in a three-level $\ensuremath{\Lambda}$ cold atomic ensemble. Moreover, both STIRAP and b-STIRAP are found to be immune to the time-varying ac Stark shift. As for a typical example to manipulate a superposition state, we realize an inverse operation on an initial superposition state, which cannot be achieved efficiently for STIRAP based on only the dark state. Our observed double STIRAP thus provides a feasible and robust manner to manipulate quantum states.
We revisit a theoretical scheme to create quantum entanglement of two three-level superconducting quantum interference devices (SQUIDs) with the help of an auxiliary SQUID. In this scenario, two three-level systems are coupled to a quantized cavity field and a classical external field and thus form dark states. The quantum entanglement can be produced by a quantum measurement on the auxiliary SQUID. Our investigation emphasizes the quantum effect of the auxiliary SQUID. For the experimental feasibility and accessibility of the scheme, we calculate the time evolution of the whole system including the auxiliary SQUID. To ensure the efficiency of generating quantum entanglement, relations between the measurement time and dominate parameters of the system are analyzed according to detailed calculations.
Achieving high-fidelity quantum state engineering is pivotal for quantum technology applications. This work investigates the Stimulated Raman Adiabatic Passage (STIRAP) protocol in a three-level Λ\LambdaΛ-system to demonstrate robust and near-perfect population transfer (∣1⟩→∣2⟩\ket{1} \to \ket{2}∣1⟩→∣2⟩). The system evolution is rigorously modeled using the \textbf{Lindblad Master Equation} to account for realistic open quantum dynamics, specifically spontaneous decay from the intermediate state ∣3⟩\ket{3}∣3⟩. We show that the \textbf{adiabatic evolution} through the Dark State, which is orthogonal to the decaying state ∣3⟩\ket{3}∣3⟩, guarantees immunity to this dissipation, achieving fidelities >0.99> 0.99>0.99. Furthermore, we analyze the protocol's resilience, mapping the fidelity landscape in the parameter space and confirming STIRAP's intrinsic robustness against control amplitude variations. This study demonstrates the efficacy and practical viability of STIRAP as a robust method for coherent population transfer in realistic noisy quantum devices.
In this paper we consider a generalization of the three-level stimulated Raman adiabatic-passage process (STIRAP). In our scheme, there are $N\ensuremath{-}1$ ground levels and one excited level. The ground levels are coupled with laser pulses through the excited level at multiphoton resonance. The ultimate aim of this scheme is to create coherent-superposition states on the ground levels. In a previous paper [J. Mod. Opt. (to be published), special issue on quantum interference] we have considered this problem from the optimal-control point of view. Here we apply a different approach: We reconsider the adiabatic approximation, which is commonly utilized to describing the STIRAP process. It is shown that in our case, in the adiabatic limit, the dark and bright subspaces of the Hamiltonian are decoupled; however, the nonadiabatic corrections influence significantly the dynamics in the dark subspace. An analytic solution is presented for the case of a five-level system. Moreover, we consider some special examples for the pulse sequences that effect prescribed final superposition states. The robustness of the scheme is studied, and the extension of our scheme is also considered.
We propose a scheme for creating coherent atomic superposition states via the technique of stimulated Raman adiabatic passage (STIRAP) in a Λ-type system where final states are composed of manifold of levels and the intermediate levels could be more than one level. If the pump pulses and Stokes pulses are kept in the same order of ordinary STIRAP, through the control the delay time between the Stokes pulses and pump pulse, we could create arbitrary superposition states in the manifold of levels.
Stimulated Raman adiabatic passage is a quantum protocol that can be used for robust state preparation in a three-level system. It has been commonly employed in quantum optics, but recently this technique has drawn attention also in circuit quantum electrodynamics. The protocol relies on two slowly varying drive pulses that couple the initial and the target state via an intermediate state, which remains unpopulated. Here we study the detrimental effect of the parasitic couplings of the drives into transitions other than those required by the protocol. The effect is most prominent in systems with almost harmonic energy level structure, such as the transmon. We show that under these conditions in the presence of decoherence there exists an optimal STIRAP amplitude for population transfer.