Chiral ground-state currents of interacting photons in a synthetic magnetic field

Journal name:
Nature Physics
Volume:
13,
Pages:
146–151
Year published:
DOI:
doi:10.1038/nphys3930
Received
Accepted
Published online

Abstract

The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields. Generating these phases in an engineered system could provide deeper insight into their nature. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall phenomena. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions through the creation of photon vacancies, or ‘holes, which circulate in the opposite direction. The combination of these key elements results in chiral ground-state currents. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons.

At a glance

Figures

  1. The unit cell for FQH and synthesizing magnetic fields.
    Figure 1: The unit cell for FQH and synthesizing magnetic fields.

    a, A schematic illustration of how qubits and their couplers can be tiled to create a two-dimensional lattice. The 3-qubit unit cell of this lattice, which is realized in this work, is highlighted. b, An optical image of the superconducting circuit made by standard nano-fabrication techniques. It consist of three superconducting qubits Qj connected via adjustable couplers CPjk. Together, they form a triangular closed loop. c, A parametric modulation approach is used for synthesizing magnetic fields. If the frequency difference of two qubits is Δ, then the sinusoidal modulation of the coupler connecting them with frequency Δ and phase φ results in an effective resonance hopping (Δ = 0) with a complex hopping amplitude between the two qubits.

  2. Single-photon circulation resulting from the TRS breaking.
    Figure 2: Single-photon circulation resulting from the TRS breaking.

    a, Schematic of the three qubits and their couplers placed in a triangular closed loop. b, The pulse sequence used for generating and circulating a microwave photon shows that the qubits frequencies ωj can be chosen to have arbitrary values, but each coupler needs to modulate with frequency Δjk, set to the difference in the qubit frequencies that it connects ωjωk. The periodic modulation of each coupler can also have a phase φjk, where ΦBφ12 + φ23 + φ31. c, A microwave photon is created by applying a π-pulse to Q1, at t = 0 (ψ0 = |100right fence). While applying the pulse sequence shown in b, the probability of a photon occupying each qubit PQj as a function of time is measured for three values of ΦB = π/2,0, π/2. We use g0 = 4MHz, ω1 = 5.8GHz, ω2 = 5.8GHz, ω3 = 5.835GHz, Δ12 = 0, Δ23 = 35MHz, Δ31 = 35MHz, φ12 = 0, φ23 = 0, and φ31 was used to set ΦB.

  3. Signature of strong interaction.
    Figure 3: Signature of strong interaction.

    a, The single-photon circulation data for ΦB = −π/2, which is shown in Fig. 2c, is partially shown for the ease of comparison with the two-photon data shown in b. b, At t = 0, two photons are created and are occupying Q1 and Q2 sites. They are generated by applying a π-pulse to Q1 and Q2 and exciting them (ψ0 = |110right fence). The parameters used, pulse sequence, and the measurements are similar to Fig. 2. While the single photon circulates in the anticlockwise direction, the photon-vacancy circulates in the clockwise direction. The counter circulation of the two-photon case compared with the single-photon case is the direct consequence of strong interactions in the system. In the absence of interactions, the direction of circulation would have been the same. These findings are schematically demonstrated in a. The yellow arrows indicate the direction of circulation of the single-photon or single-vacancy case, where photons and vacancies are depicted by bright and dark disks, respectively, and shown on top of the optical image of the circuit used.

  4. Chiral currents in the ground state.
    Figure 4: Chiral currents in the ground state.

    a, The pulse sequence for adiabatically preparing the ground state of equation (2). For ground states in the single-photon manifold, Q1 is excited at t = 0 (ψ0 = |100right fence), and in the two-photon manifold, Q1 and Q2 are excited (ψ0 = |110right fence). To measure ÎQ1 → Q2 at the end of parameter ramping, Q1 and Q2 are rotated, allowing for measurements of left fenceσQ1XσQ2Yright fence and left fenceσQ1YσQ2Xright fence. b, The measured values of left fenceÎchiralright fence in the single-photon (olive colour) or two-photon manifolds (maroon colour). The solid lines are computations for Tadia right arrow . The energy gap of the Hamiltonian of the system (equation (2)) as a function of ΦB is numerically computed and is shown as the background of the data. The gap closes at ΦB = 0, ±2π and the ground state becomes degenerate (green regions). The maximum gap size is 3g0, which here is 12MHz.

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Author information

  1. These authors contributed equally to this work.

    • P. Roushan,
    • C. Neill &
    • A. Megrant

Affiliations

  1. Google Inc., Santa Barbara, California 93117, USA

    • P. Roushan,
    • A. Megrant,
    • Y. Chen,
    • R. Barends,
    • A. Fowler,
    • E. Jeffrey,
    • J. Kelly,
    • E. Lucero,
    • J. Mutus,
    • M. Neeley,
    • D. Sank,
    • T. White &
    • J. Martinis
  2. Department of Physics, University of California, Santa Barbara, California 93106, USA

    • C. Neill,
    • B. Campbell,
    • Z. Chen,
    • B. Chiaro,
    • A. Dunsworth,
    • P. J. J. OMalley,
    • C. Quintana,
    • A. Vainsencher,
    • J. Wenner &
    • J. Martinis
  3. Google Inc., Los Angeles, California 90291, USA

    • R. Babbush &
    • H. Neven
  4. The Graduate Center, CUNY, New York, New York 10016, USA

    • E. Kapit
  5. Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA

    • E. Kapit

Contributions

P.R., C.N. and A.M. performed the experiment. E.K. provided theoretical assistance. P.R. analysed the data, and with C.N. and E.K. co-wrote the manuscript and Supplementary Information. All of the UCSB and Google team members contributed to the experimental set-up. All authors contributed to the manuscript preparation.

Competing financial interests

The authors declare no competing financial interests.

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