Realization of a $\mathrm{\ensuremath{\Lambda}}$ System with Metastable States of a Capacitively Shunted Fluxonium

Realization of a $Λ$ System with Metastable States of a Capacitively Shunted Fluxonium

N. Earnest, S. Chakram, Y. Lu, N. Irons, R. K. Naik, N. Leung, L. Ocola, D. A. Czaplewski, B. Baker, Jay Lawrence, Jens Koch, and D. I. Schuster

Phys. Rev. Lett. 120, 150504 – Published 13 April 2018

Abstract

We realize a $Λ$ system in a superconducting circuit, with metastable states exhibiting lifetimes up to 8 ms. We exponentially suppress the tunneling matrix elements involved in spontaneous energy relaxation by creating a “heavy” fluxonium, realized by adding a capacitive shunt to the original circuit design. The device allows for both cavity-assisted and direct fluorescent readouts, as well as state preparation schemes akin to optical pumping. Since direct transitions between the metastable states are strongly suppressed, we utilize Raman transitions for coherent manipulation of the states.

Received 12 July 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.150504

Physics Subject Headings (PhySH)

Coherent control Optical pumping Quantum computation Quantum control Quantum memories

Superconducting qubits

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

N. Earnest^1,*, S. Chakram¹, Y. Lu¹, N. Irons², R. K. Naik¹, N. Leung¹, L. Ocola³, D. A. Czaplewski³, B. Baker², Jay Lawrence⁴, Jens Koch², and D. I. Schuster^1,†

¹The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
²Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
³Argonne National Laboratories, Center for Nanoscale Materials, Argonne, Illinois 60439, USA
⁴Department of Physics, Dartmouth College, Hanover, New Hampshire 03755, USA

^*nearnest@uchicago.edu
^†david.schuster@uchicago.edu

Demonstration of Protection of a Superconducting Qubit from Energy Decay

Yen-Hsiang Lin, Long B. Nguyen, Nicholas Grabon, Jonathan San Miguel, Natalia Pankratova, and Vladimir E. Manucharyan

Phys. Rev. Lett. 120, 150503 (2018)

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Vol. 120, Iss. 15 — 13 April 2018

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Figure 1
(a) Equivalent circuit diagram of the heavy fluxonium capacitively coupled to a readout resonator (Supplemental Material [26]). (b) Scanning electron microscope image of the device, with a magnified view of the 100 Josephson junction array, fabricated using the bridgeless method detailed in [27]. (c) Simulated potential energy landscape or wave function at $Φ_{ext} = 0.02 Φ_{0}$ demonstrating localized wave functions in three wells. (d) Simulated potential energy landscape at $Φ_{ext} = 0.51 Φ_{0}$ , where $| g_{0} ⟩$ and $| g_{1} ⟩$ are nearly degenerate.
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Figure 2
Single-tone spectroscopy of the fluxonium-resonator system in the vicinity of the resonator and primary plasmon transition frequencies. Dashed lines indicate simulated energy levels of the coupled system based on device parameters extracted from fits to single and two-tone spectra. Transitions that change rapidly with flux are interwell fluxon transitions, while the flatter transitions are intrawell plasmon transitions. Left inset: interference due to coupling between the ground and excited states of neighboring wells. Right inset: features associated with fluxon transitions crossing with the resonator. The spectrum is normalized by the transmission amplitude of the bare resonator (Supplemental Material [26]).
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Figure 3
(a) Two-tone spectroscopy showing direct fluxon transitions (orange and green lines) and two-photon transitions to the two-excitation manifold ( $| f_{0} ⟩$ , $| e_{- 1} ⟩$ , $| e_{1} ⟩$ ). State labeling for the transitions is valid for $Φ_{ext} > 0$ . The $| f_{0} ⟩$ level serves as the intermediate state in a $Λ$ system comprising the ground state $| g_{0} ⟩$ and the metastable $| g_{1} ⟩$ state, and assists in Raman transitions. (b) Pump-probe spectroscopy of Raman transitions between $| g_{0} ⟩$ and $| g_{1} ⟩$ as a function of pump (near $| g_{0} ⟩ \to | f_{0} ⟩ - 2 γ$ transition) and probe frequency (near $| g_{1} ⟩ \to | f_{0} ⟩$ ). The Raman transition is seen when $2 ν_{pump} - ν_{probe} = E_{g_{1}} - E_{g_{0}}$ , represented by the dashed line. The upper-left inset shows wave functions of the states involved in the transition. The intermediate $| f_{0} ⟩$ state couples to $| g_{0} ⟩$ via a two-photon process and has a small amplitude in the right well, with a direct dipole-allowed transition to the metastable $| g_{1} ⟩$ state. The dashed lines are simulated energy levels of the fluxonium-resonator system. The color bar is normalized by the transmission of the bare resonator.
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Figure 4
(a) Energy relaxation time ( $T_{1}$ ) as a function of magnetic flux measured through a combination of direct drive to a mixed state, plasmon pumping, and Raman transitions. The dashed purple line indicates the inverse square of the charge matrix element of the fluxon transition of interest. The inset shows the $T_{1}$ decay curve of the point indicated by the red star, after driving to a mixed state following a long Raman drive. (b) Rabi chevron obtained by detuning the probe-drive tone away from the Raman transition described in Fig. 3 at $Φ_{ext} = 0.078 Φ_{0}$ . The Raman transition is chosen to be 60 MHz from the $| f 0 ⟩$ level and the peak $π$ pulse fidelity is $\sim 90 %$ . (c) Ramsey experiment at $Φ_{ext} = 0.078 Φ_{0}$ , obtained using $π / 2$ pulses extracted from Rabi drive of the Raman transition resulting in a $T_{2}^{*}$ of 500–550 ns.
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Physical Review Letters

Realization of a $Λ$ System with Metastable States of a Capacitively Shunted Fluxonium

N. Earnest, S. Chakram, Y. Lu, N. Irons, R. K. Naik, N. Leung, L. Ocola, D. A. Czaplewski, B. Baker, Jay Lawrence, Jens Koch, and D. I. Schuster

Phys. Rev. Lett. 120, 150504 – Published 13 April 2018

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Demonstration of Protection of a Superconducting Qubit from Energy Decay

Yen-Hsiang Lin, Long B. Nguyen, Nicholas Grabon, Jonathan San Miguel, Natalia Pankratova, and Vladimir E. Manucharyan

Phys. Rev. Lett. 120, 150503 (2018)

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Physical Review Letters

Realization of a Λ System with Metastable States of a Capacitively Shunted Fluxonium

N. Earnest, S. Chakram, Y. Lu, N. Irons, R. K. Naik, N. Leung, L. Ocola, D. A. Czaplewski, B. Baker, Jay Lawrence, Jens Koch, and D. I. Schuster

Phys. Rev. Lett. 120, 150504 – Published 13 April 2018

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

See Also

Demonstration of Protection of a Superconducting Qubit from Energy Decay

Yen-Hsiang Lin, Long B. Nguyen, Nicholas Grabon, Jonathan San Miguel, Natalia Pankratova, and Vladimir E. Manucharyan

Phys. Rev. Lett. 120, 150503 (2018)

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Realization of a $Λ$ System with Metastable States of a Capacitively Shunted Fluxonium