Photon Transport in a Bose-Hubbard Chain of Superconducting Artificial Atoms

G. P. Fedorov, S. V. Remizov, D. S. Shapiro, W. V. Pogosov, E. Egorova, I. Tsitsilin, M. Andronik, A. A. Dobronosova, I. A. Rodionov, O. V. Astafiev, and A. V. Ustinov

Phys. Rev. Lett. 126, 180503 – Published 7 May 2021

Abstract

We demonstrate nonequilibrium steady-state photon transport through a chain of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard model. Using transmission spectroscopy, we show that the system retains many-particle coherence despite being coupled strongly to two open spaces. We find that cross-Kerr interaction between system states allows high-contrast spectroscopic visualization of the emergent energy bands. For vanishing disorder, we observe the transition of the system from the linear to nonlinear regime of photon blockade in excellent agreement with the input-output theory. Finally, we show how controllable disorder introduced to the system suppresses nonlocal photon transmission. We argue that proposed architecture may be applied to analog simulation of many-body Floquet dynamics with even larger arrays of artificial atoms paving an alternative way towards quantum supremacy.

Received 15 December 2020
Accepted 16 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.180503

Physics Subject Headings (PhySH)

Many-body localization Open quantum systems & decoherence Quantum simulation Quantum transport Superconducting quantum optics

Superconducting qubits

Bose-Hubbard model Microwave techniques

Atomic, Molecular & OpticalGeneral PhysicsQuantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

G. P. Fedorov ^1,2,3,*, S. V. Remizov^4,5, D. S. Shapiro^4,5, W. V. Pogosov^4,6, E. Egorova ^1,2,3, I. Tsitsilin ^1,2,3, M. Andronik ⁷, A. A. Dobronosova^7,4, I. A. Rodionov^7,4, O. V. Astafiev^8,1,9,10, and A. V. Ustinov ^2,11,3

¹Moscow Institute of Physics and Technology, 141701 Dolgoprundiy, Russia
²Russian Quantum Center, National University of Science and Technology MISIS, 119049 Moscow, Russia
³National University of Science and Technology MISIS, 119049 Moscow, Russia
⁴Dukhov Automatics Research Institute, (VNIIA), 127055 Moscow, Russia
⁵Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 125009 Moscow, Russia
⁶Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, 125412 Moscow, Russia
⁷FMN Laboratory, Bauman Moscow State Technical University, 105005 Moscow, Russia
⁸Skolkovo Institute of Science and Technology, 121205 Moscow, Russia
⁹Physics Department, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
¹⁰National Physical Laboratory, Teddington TW11 0LW, United Kingdom
¹¹Physics Institute and Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany

^*gleb.fedorov@phystech.edu

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Issue

Vol. 126, Iss. 18 — 7 May 2021

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Images

Figure 1
(a) Optical image of the device (false colored). Input and output waveguides (beige) are strongly coupled to the edge transmons (green). All transmons can be dispersively read out via auxiliary resonators (orange) and tuned via flux bias lines (red). (b) Model of the device—a B-H lattice with five sites. Bosons are inserted from the left by the drive of strength $Ω$ and leak predominantly from the sides at rate $Γ$ . The energy of an ith localized boson is $ℏ ω_{i}$ , adding another boson to the same site costs $ℏ α_{i} < 0$ . Bosons can tunnel between sites at rate $J$ . (c) Schematic of the measurement setup: the direct transmission spectroscopy (DTS) is done using the vector network analyzer which measures the complex transmission $S_{21}$ . The cross-Kerr spectroscopy (CKS) requires an additional microwave source connected through a directional coupler. (d) CKS is done by sweeping the source frequency (blue arrow) while monitoring the transmission at a certain resonance peak via the VNA (red arrow).
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Figure 2
(a) DTS of the chain. $S_{21}$ includes the attenuation and amplification in the measurement chain, VNA output power is shown on the right. In the top row, black lines are the fit of the lowest five transitions of Eq. (1) for $J / 2 π = 41 MHz$ , $ω_{i} / 2 π \approx 4.05 GHz$ . (b) CKS via the third mode showing the emergent band structure of the system. Dashed lines fit the frequencies of the purely quantum transitions.
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Figure 3
(a) The analytical solution for the $S_{21}$ in the linear regime (smooth curves) fitted to the low power data (clouds), normalized. (b) Experimental and simulated $| S_{21} |$ for various driving powers. Driving power is calibrated to match the Rabi frequency $Ω$ of the simulation. Dashes show the corresponding multiphoton transition frequencies calculated using the eigenlevels from (c). (c) The energy level structure of the model with and without interaction using the parameters extracted from the fits; three excitations per site are included, and up to four excitations total; $E_{n}$ is the energy of the $n$ th eigenstate, $E_{0} = 0$ . (d) Relevant many-body eigenstates projected onto the unperturbed basis [colors as in (c)]. The inherent randomness in the decompositions of the high-energy states conditions the random structure of the energy levels.
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Figure 4
(a) Raw transmission data for $σ = 6$ , 40 MHz and 100 realizations of disorder; absolute value of the transmission is shown with color. (b) Localization and disappearance of transmission with increasing disorder. Each curve shows the absolute value of the averaged transmission over the Gaussian disorder realizations with a certain standard deviation $σ$ shown in the legend. Each next curve is offset downwards for better visibility. (c) Probability distributions of the brightest peak prominence $⟨ | S_{21} |^{\max} ⟩$ (see text) observed in the disorder realizations for the $σ$ values from (b).
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