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

Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging collective effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half-filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in Zanner et al. [Nat. Phys. 18, 538 (2022)] and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.

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“…An array of L uncoupled transmons [8] is described accurately by the Bose-Hubbard Hamiltonian [16,28,29,33],…”

Section: A Transmon Arraymentioning

confidence: 99%

Collective bosonic effects in an array of transmon devices

et al. 2022

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“…At last, one may consider the situation where the spectral density of the colored noise is given by the δ-function, i.e., we have a periodic driving. Experimentally, this case is realized, for example, in the chain of the capacitively coupled transmons where the first transmon is excited by a microwave generator [6][7][8], or in the array of optical cavities with the Kerr nonlinearity where the first cavity is excited by a laser. We mentioned that the minimal size chains consisting of two cavities is currently used to study a number of other fundamental problems [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Ballistic transport of interacting Bose particles in the tight-binding chain

Muraev¹,

Maksimov²,

Kolovsky³

2022

Preprint

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It is known that quantum transport of non-interacting Bose particles across the tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local non-linear oscillators. It is also argued that, unlike the case of non-interacting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in course of time. An estimate for the decay time is obtained.

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“…It serves as the model for the Josephson oscillation (periodic change in occupations of the lattice sites) and the self-trapping (interactioninduced destruction of the inter-site tunneling) [1][2][3][4], semiclassical quantization of the many-body systems [5,6], highly correlated states like fragmented condensates and NOON state [7][8][9][10][11], and the excited state quantum phase transitions [12][13][14]. From the experimental viewpoint the BH dimer can be realized by using several platforms among which are cold atoms in a two-well optical potential [3,4,14], two coupled optical microcavities with Kerr nonlinearity [15,16], and two capacitively coupled transmons [17,18]. Notice that the last two systems do not conserve the number of particles and, thus, they should be described in the framework of the open or dissipative Bose-Hubbard model [19,20].…”

mentioning

confidence: 99%

“…The particle exchange with reservoirs enriches the dynamics of the BH dimer, leading to several new effects which are not present in the conservative BH dimer. These are the resonant transmission [18,21] and the quantum manifestation of bifurcations in the classical driven-dissipative dimer [16,22,23]. The latter research direction also includes analysis of the true steady-state of the system, as well as the metastable states which are responsible for hysteresis in the quantum case [24,25].…”

mentioning

confidence: 99%

Josephson oscillation in the dissipative Bose-Hubbard dimer

Kolovsky¹

2022

Preprint

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We analyze Josephson's oscillation of Bose particles in the open (dissipative) Bose-Hubbard dimer. First, we excite the dimer from the vacuum state into a state suitable for observing the oscillation by using a special protocol for external driving. Next, we switch off the driving and observe the oscillation. It is shown that the main mechanism for the decay of Josephson's oscillation is the dephasing due to fluctuating number of particles in open systems. An analytical estimate for the decay time is obtained.

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

Cited by 46 publications

References 40 publications

Collective bosonic effects in an array of transmon devices

Collective bosonic effects in an array of transmon devices

Ballistic transport of interacting Bose particles in the tight-binding chain

Josephson oscillation in the dissipative Bose-Hubbard dimer

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