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Electromagnetically induced interference in a superconducting flux qubit
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10.1063/1.4811251
/content/aip/journal/ltp/39/6/10.1063/1.4811251
http://aip.metastore.ingenta.com/content/aip/journal/ltp/39/6/10.1063/1.4811251
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) Schematic energy diagram of a driven two-level system. The dotted curve represents the strong driving field  cos ω. The field through the tunnel coupling Δ forms a LZS interference, exchanging photons with the qubit. (b) Quantum tunnel coupling exists between states and . The interaction between a qubit and an electromagnetic system (such as the environment bath or a single-mode electromagnetic field) would form new couplings between the two states.

Image of FIG. 2.
FIG. 2.

Schematic energy diagram of relaxation induced interference: (a) refers to the transition from state to through ; (b) refers to the transition from state to through . The dashed red upward arrows mark the multiphoton absorption from the driving microwave field while the dashed green downward arrows mark the multiphoton release to the microwave. The dotted arrows describe the energy released or absorbed by the bath. Effectively, the resonant conditions are ω = ε + ω (from state to ) and ω = ε – ω (from state to ). The blue region I describes effective phase difference contributing to the interference at . The yellow region II expresses the phase eliminated by the bath. The green region III expresses the effective phase difference contributing to the interference at .

Image of FIG. 3.
FIG. 3.

The stationary population of relaxation induced interference. The pattern is obtained from Eq. (15) . (a) The characteristic frequency ω/2π = 0.05 GHz with the temperature 20 mK. Features of population inversion and periodical modulation are notable. (b) The characteristic frequency ω/2π = 6 GHz with the temperature 20 mK. (c) The characteristic frequency ω/2π = 0.05 GHz with the temperature 2·10 mK. The driving frequency ω/2π = 0.6 GHz.

Image of FIG. 4.
FIG. 4.

Calculated final qubit population versus energy detuning and microwave amplitude. (a) The stationary interference pattern in the weak relaxation situation. The parameters we used are the driving frequency ω/2π = 0.6 GHz, the dephasing rate Г/2π = 0.06 GHz, the couple tunneling Δ/2π = 0.013 GHz, αϕ = 0.0002, the temperature is 20 mK, and the characteristic frequency ω/2π = 0.05 GHz. The periodical patterns of RII can be seen, although not clear. (b) The stationary interference pattern in the strong relaxation situation with αϕ = 0.02 and ω/2π = 0.05 GHz. Since the relaxation strength is stronger, the periodical interference patterns are more notable. (c) The stationary interference pattern in the weak relaxation situation with αϕ = 0.000002 and ω/2π = 6 GHz. (d) The stationary interference pattern in the strong relaxation situation with αϕ = 0.0002 and ω/2π = 6 GHz. (e) The unsaturated interference pattern in the weak relaxation situation. The system dynamics time  = 0.5 s. The characteristic frequency ω/2π = 0.05 GHz, αϕ = 0.0002. (f) The unsaturated interference pattern in the weak relaxation situation. The system dynamics time  = 0.5 s. The characteristic frequency ω/2π = 6 GHz, αϕ = 0.000002. (g) The unsaturated interference pattern in the strong relaxation situation. The system dynamics time  = 0.5 s. The characteristic frequency ω/2π = 0.05 GHz, α ϕ = 0.02. (h) The unsaturated interference pattern in the strong relaxation situation. The dynamics time  = 0.5 s. The characteristic frequency ω/2π = 6 GHz, αϕ = 0.0002. The other parameters used in these figures are the same with those in Fig. 4a .

Image of FIG. 5.
FIG. 5.

(a) The unsaturated interference pattern obtained by phenomenological relaxation theory. The system dynamics time is 0.5 s, Г/2π= 0.000008 GHz. (b) The stationary interference pattern obtained by the phenomenological relaxation theory. Г/2π = 0.000008 GHz. (c) Comparison of the results of two theories. The blue dashed line expresses the population in with the characteristic frequency ω/2π = 6 GHz, the microwave amplitude is fixed at 8 GHz, αϕ = 0.000002 and the system dynamics time  = 13 s, the red dotted line expresses the population with the characteristic frequency ω/2π = 0.05 GHz, the microwave amplitude is fixed at 8 GHz, αϕ = 0.0002, and the system dynamics time  = 16 s. The black line uses the stationary result with the phenomenological relaxation theory with Г/2π = 0.000008 GHz, and the microwave amplitude is fixed at 8 GHz. (d) The unsaturated interference pattern obtained by phenomenological relaxation theory. The evolution time is 0.5 s, Г/2π = 0.001 GHz. (e) The stationary interference pattern obtained by phenomenological relaxation theory. Г/2π = 0.001 GHz. Other parameters are identical with those of Fig. 4a .

Image of FIG. 6.
FIG. 6.

Schematic energy diagram of a strongly driven two-level system interacting with a weak single-mode field. The green solid curve represents the weak field, forming effective coupling between states and .

Image of FIG. 7.
FIG. 7.

(a) and (b) Schematic energy diagram of Rabi-oscillation-induced interference: (a) describes the transition from state to ; (b) describes the transition from state to . (c), (d), and (e) The interference pattern of population in state obtained from Eqs. (26) , (27) , and (28) , respectively. The parameters used here are ω/2π = 2 GHz,  = 0.9, Г/2π = 0.000008 GHz and the temperature is 20 mK. Other parameters of the qubit are identical with Fig. 4a .

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/content/aip/journal/ltp/39/6/10.1063/1.4811251
2013-06-27
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Electromagnetically induced interference in a superconducting flux qubit
http://aip.metastore.ingenta.com/content/aip/journal/ltp/39/6/10.1063/1.4811251
10.1063/1.4811251
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