Ramsey-like spectroscopy of superconducting qubits with dispersive evolution

Yan Zhang, Tiantian Huan, Ri-gui Zhou, and Hou Ian

Phys. Rev. A 102, 013710 – Published 9 July 2020

Abstract

We proposed a spectroscopic method that extends Ramsey's atomic spectroscopy to detect the transition frequency of a qubit fabricated on a superconducting circuit. The method uses a multi-interval train of qubit biases to implement an alternate resonant and dispersive couplings to an incident probe field. The consequent absorption spectrum of the qubit has a narrower linewidth at its transition frequency than that obtained from constantly biasing the qubit to resonance while the middle dispersive evolution incurs only a negligible shift in detected frequency. Modeling on transmon qubits, we find that the linewidth reduction reaches 23% and Ramsey fringes are simultaneously suppressed at extreme duration ratio of dispersion over resonance for a double-resonance scheme. If the scheme is augmented by an extra resonance segment, a further 37% reduction can be achieved.

Received 22 April 2020
Revised 2 June 2020
Accepted 15 June 2020

DOI:https://doi.org/10.1103/PhysRevA.102.013710

Physics Subject Headings (PhySH)

Electronic transitions Quantum measurements Quantum optics with artificial atoms

Superconducting qubits

Atomic, Molecular & OpticalInterdisciplinary PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yan Zhang ¹, Tiantian Huan¹, Ri-gui Zhou ², and Hou Ian ^1,*

¹Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China
²College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China

^*houian@um.edu.mo

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Vol. 102, Iss. 1 — July 2020

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Images

Figure 1
(a) The equivalent circuit network of the transmon qubit and its surroundings. Two parallel Josephson junctions of junction energy $E_{J}$ and capacitance $C_{J}$ are connected to a gate capacitor of capacitance $C_{g}$ and shunted to the ground through a capacitor of capacitance $C_{B}$ . The transmon is biased through both a DC offset $V_{g}$ and a magnetic flux $Φ_{ext}$ . Ramsey biasing is realized through current pulses of particular durations in the flux bias loop. (b) The pulse sequences at the waveguide input and at the flux bias to furnish the Ramsey resonance scheme: $V_{rf}$ is set to feed a square pulse whose length matches the total time duration of the biasing train; $Φ_{ext}^{(1)}$ illustrates the scenario for a double-resonance scheme and $Φ_{ext}^{(2)}$ for a triple-resonance scheme. The effectiveness of the two differing schemes for spectroscopy is depicted in the figures below.
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Figure 2
The transition probability of a transmon qubit as a function of probe field frequency $ω / 2 π$ at three values of $s$ between $0.68 π / 3.5 η$ and $0.68 π / 2.5 η$ , given as the family of solid curves (colored from top to bottom in the same ascending order of $s$ magnitude shown in the legend). The dashed line, which corresponds to the spectrum of CW detection under the same system parameters, serves as a reference.
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Figure 3
Phase shift $ζ$ experienced by the detection pulse for double-resonance Ramsey biasing. The color coding follows that of Fig. 2, where the ascending order of $s$ magnitude associates with the curves from bottom to top. Under all three values of $s$ , the phase shifts are positive but small at the resonance frequency while dipping symmetrically into the negative values in the close vicinity of resonance. When $s$ becomes sufficiently small (overall interaction duration shortened), the shift peaking at resonance splits up and opens a dipping window in the middle. The glitches are the artifacts of numerical integration.
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Figure 4
(a) The transition probability under the triple-resonance scheme at three different values of $s$ (solid curves) compared to the double-resonance scheme (dashed curve, $s = 0.68 π / 3 η$ ). The solid curves are color coded from bottom to top, following the ascending order of $s$ magnitude given in the legend. (b) $〈P_{e}^{res}〉$ under close-resonance approximation $s = 0.68 π / 2 η$ (solid curve) compared to one without approximation (dashed curve).
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Figure 5
Phase shift $ζ$ for triple-resonance scheme, where $s$ adopts the same three values of Fig. 4. The curves from bottom to top associate with the ascending order of $s$ magnitude shown in the legend. For all $s$ , the shifts are slightly asymmetric about the resonance point and are nonpositive over an expanded range of frequency.
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