Transcript Slide 1
Dynamics and decoherence of a qubit coupled to a two-level system S. Ashhab1, J. R. Johansson1 and Franco Nori1,2 1Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama, Japan 2Center for Theoretical Physics, CSCS, Department of Physics, University of Michigan, Ann Arbor, Michigan, USA Summary We study the effects of an uncontrollable quantum two-level system (TLS) on the qubit dynamics. We consider both the decoherence dynamics and the qubit’s response to an oscillating external field. Model of qubit-environment Decoherence dynamics Hamiltonian: Outside dashed line: We only need to know S(w). Master equation: Inside dashed line: We need to know exact nature of the noise sources. Trace out TLS Density matrix of entire system Qubit dynamics. Q1: When can we use the classical picture? Results: 1 - Weakly vs. strongly dissipative TLS Dephasing Relaxation Q2: What happens if we try to drive Rabi oscillations in the qubit? Rabi oscillations Energy levels in dressed-state picture: Longer TLS T1, T2 More memory Non-markovian behavior Focus on one quantum TLS. a) G G TLS q Short transient time ~ 1/GTLS followed by exponential decay. I.e., the steady state is an exponential decay with a corrected Gq. b) G TLS G q Transient time ~ 1/GTLS comparable to decoherence time (1/Gq). A steady state exponential decay is almost reached. c) G TLS G q Estimated transient time ~ 1/GTLS exceeds decoherence time (1/Gq). Qubit decay cannot be described in terms of exponential decay functions, i.e., no G1q and G2q. Results: 2 – Weakly vs. strongly coupled TLS When the coupling strength is larger than all decoherence rates in the problem Strong coupling. Expected result: Rabi resonance peak splits into two when coupling strength is increased. Otherwise Weak coupling. Results: 3 – Comparison with traditional weak-coupling approximation Traditional weak-coupling approximation Y-axis: Maximum qubit excitation probability between t=0 and t=20p/W0. Additional results: 1) Zero detuning peak: two-photon process flipping both qubit and TLS states. 2) Dips in resonance-peak structure: these occur when some of the oscillation frequencies are integer multiples of each other. 3) Asymmetry between the two main peaks: lower-frequency peak has a larger contribution from the two-photon process. With decoherence: Solid line: no decoherence. G1 Green: analytic expression in traditional weakcoupling approximation l2 sin 2 q sin 2 TLS 2G2TLS 1 G2 G1 2 Perturbation theory in quantum picture l sin q sin TLS 2 G1 G2 2 Blue: analytic expression in weakcoupling limit of quantum picture G1 Largest G 2 2(G2TLS G2q G1q ) Weak coupling l2 sin 2 q sin 2 TLS 4(G TLS 2 Red: numerical simulation of quantum picture G ) q 2 Strong coupling l (coupling strength) The two approaches differ when the condition: G TLS G q is not satisfied. Dashed line: strong TLS decoherence TLS becomes weakly coupled. Dotted line: moderate decoherence on both. Narrow features are suppressed. Supported in part by the Frontier Research System at RIKEN, JSPS, the US AFOSR, ARDA, NSA, and the US National Science Foundation. Dash-dotted line: strong qubit decoherence. Qubit cannot perform Rabi oscillations. cond-mat/0512677 and cond-mat/0602577. Corresponding author: Sahel Ashhab, [email protected]