Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1006.2935 · New Journal of Physics

Bose–Hubbard dynamics of polaritons in a chain of circuit quantum electrodynamics cavities

Martin Leib, Michael J Hartmann

Published Sep 22, 2010• 93 citations
arXivHTMLPDF

Abstract

We investigate a chain of superconducting stripline resonators, each interacting with a transmon qubit, that are capacitively coupled in a row. We show that the dynamics of this system can be described by a Bose–Hubbard Hamiltonian with attractive interactions for polaritons, superpositions of photons and qubit excitations. This setup, we envisage, is one of the first platforms where all the technological components that are needed to experimentally study chains of strongly interacting polaritons have already been realized. By driving the first stripline resonator with a microwave source and detecting the output field of the last stripline resonator, one can spectroscopically probe the properties of the system in the driven dissipative regime. We calculate the stationary polariton density and density–density correlations g (2) for the last cavity, which can be measured via the output field. Our results display a transition from a coherent to a quantum field as the ratio of on-site interactions to driving strength is increased.

DOI
10.1088/1367-2630/12/9/093031

Related papers

The circuit quantum electrodynamical Josephson interferometer

Robert Jirschik, Michael J. Hartmann

Arrays of circuit cavities offer fascinating perspectives for exploring quantum many-body systems in a driven dissipative regime where excitation losses are continuously compensated by coherent input drives. Here we investigate a system consisting of three transmission line resonators, where the two outer ones are driven by coherent input sources and the central resonator interacts with a superconducting qubit. Whereas a low excitation number regime of such a device has been considered previously with a numerical integration, we here specifically address the high excitation density regime. We present analytical approximations to these regimes in the form of two methods. The first method is a Bogoliubov or linear expansion in quantum fluctuations which can be understood as an approximation for weak nonlinearities. As the second method we introduce a combination of mean-field decoupling for the photon tunneling with an exact approach to a driven Kerr nonlinearity which can be understood as an approximation for low tunneling rates. In contrast to the low excitation regime we find that for high excitation numbers the anti-bunching of output photons from the central cavity does not monotonously disappear as the tunnel coupling between the resonators is increased.

arXiv:1309.5358•EPJ Quantum Technology•Jan 29, 2014•1 citation

Interaction-induced hopping phase in driven-dissipative coupled photonic microcavities

S. R. K. Rodríguez, Alberto Amo, Isabelle Sagnes +4 more

The Bose-Hubbard model (BHM) describes bosons hopping across sites and interacting on-site. Inspired by the success of BHM simulators with atoms in optical lattices, proposals for implementing the BHM with photons in coupled nonlinear cavities have recently emerged. Two coupled semiconductor microcavities constitute a model system where the hopping, interaction and decay of exciton polaritons-mixed light-matter quasiparticles-can be engineered in combination with site-selective coherent driving to implement the driven-dissipative two-site optical BHM. Here we explore the interplay of interference and nonlinearity in this system, in a regime where three distinct density profiles can be observed under identical driving conditions. We demonstrate how the phase acquired by polaritons hopping between cavities can be controlled through polariton-polariton interactions. Our results open new perspectives for synthesizing density-dependent gauge fields using polaritons in two-dimensional multicavity systems.

arXiv:1602.07114•Nature Communications•Jun 16, 2016•102 citations

Circuit quantum electrodynamics with a nonlinear resonator

Patrice Bertet, Florian R. Ong, M. Boissonneault +6 more

One of the most studied model systems in quantum optics is a two-level atom strongly coupled to a single mode of the electromagnetic field stored in a cavity, a research field named cavity quantum electrodynamics or CQED. CQED has recently received renewed attention due to its implementation with superconducting artificial atoms and coplanar resonators in the so-called circuit quantum electrodynamics (cQED) architecture. In cQED, the couplings can be much stronger than in CQED due to the design flexibility of superconducting circuits and to the enhanced field confinement in one-dimensional cavities. This enabled the realization of fundamental quantum physics and quantum information processing experiments with a degree of control comparable to that obtained in CQED. The purpose of this chapter is to investigate the situation where the resonator to which the atom is coupled is made nonlinear with a Kerr-type nonlinearity, causing its energy levels to be nonequidistant. The system is then described by a nonlinear Jaynes-Cummings Hamiltonian. This considerably enriches the physics since a pumped nonlinear resonator displays bistability, parametric amplification, and squeezing. The interplay of strong coupling and these nonlinear effects constitutes a novel model system for quantum optics that can be implemented experimentally with superconducting circuits. This chapter is organized as follows. In a first section we present the system consisting of a superconducting Kerr nonlinear resonator strongly coupled to a transmon qubit. In the second section, we describe the response of the sole nonlinear resonator to an external drive. In the third section, we show how the resonator bistability can be used to perform a high-fidelity readout of the transmon qubit. In the last section, we investigate the quantum backaction exerted by the intracavity field on the qubit.

arXiv:1111.0501•Nov 2, 2011•2 citations

Soliton versus single-photon quantum dynamics in arrays of superconducting qubits

Ben Blain, Giampiero Marchegiani, Juan Polo +2 more

Superconducting circuits constitute a promising platform for future implementation of quantum processors and simulators. Arrays of capacitively coupled transmon qubits naturally implement the Bose-Hubbard model with attractive on-site interaction. The spectrum of such many-body systems is characterized by low-energy localized states defining the lattice analog of bright solitons. Here, we demonstrate that these bright solitons can be pinned in the system, and we find that a soliton moves while maintaining its shape. Its velocity obeys a scaling law in terms of the combined interaction and number of constituent bosons. In contrast, the source-to-drain transport of photons through the array occurs through extended states that have higher energy compared to the bright soliton. For weak coupling between the source or drain and the array, the populations of the source and drain oscillate in time; for chains of even length, their population remains low at all times, while it can reach half the number of total bosons in odd chains. Implications of our results for actual experimental realizations are discussed.

arXiv:2212.06627•Physical Review Research•Aug 25, 2023•5 citations

Characterizing polariton states in the nondispersive regime of circuit quantum electrodynamics

Arvind Mamgain, Samarth Hawaldar, Athreya Shankar +1 more

A superconducting qubit coupled to a readout resonator is currently the building block of multiple quantum computing as well as quantum optics experiments. A typical qubit-resonator system is coupled in the dispersive regime, where the detuning between qubit and resonator is much greater than the coupling between them. In this work, we fabricated and measured a superconducting transmon-resonator system in the nondispersive regime. The dressed states formed by the mixing of the bare qubit and resonator states can be further mixed by applying a drive on the qubit, leading to the formation of polariton states. We report experimental studies of transitions between polariton states at varying driving powers and frequencies and show how the nondispersive coupling of the higher levels of the qubit-resonator system modifies the polariton eigenstates and the corresponding transition frequencies. We also report close agreement with numerical results obtained from a driven Jaynes-Cummings model beyond the dispersive regime.

arXiv:2302.04523•Physical Review A•Sep 5, 2023•3 citations

Coherent Polariton Dynamics in Coupled Highly Dissipative Cavities

Yong‐Chun Liu, Xingsheng Luan, Haokun Li +3 more

The coherent light-matter interaction at the single-photon and electronic qubit level promises to be a remarkable potential for nonclassical information processing. Besides the efforts of improving the figure of merit of the cavities, here we demonstrate strong anharmonicity in the polariton dressed states via dark state resonances in a highly dissipative cavity. It is shown that the vacuum Rabi oscillation occurs for a single quantum emitter inside a cavity even with the bosonic decay-to-interaction rate ratio exceeding ${10}^{2}$, when the photon field is coupled to an auxiliary high-$Q$ cavity. Moreover, photon blockade is observable in such a highly dissipative cavity quantum electrodynamics system. This study provides a promising platform for overcoming decoherence and advancing the coherent manipulation of polariton qubits.

arXiv:1405.3473•Physical Review Letters•May 30, 2014•85 citations
We investigate a chain of superconducting stripline resonators, each interacting with a transmon qubit, that are capacitively coupled in a row. We show that the dynamics of this system can be described by a Bose–Hubbard Hamiltonian with attractive interactions for polaritons, superpositions of photons and qubit excitations. This setup, we envisage, is one of the first platforms where all the technological components that are needed to experimentally study chains of strongly interacting polaritons have already been realized. By driving the first stripline resonator with a microwave source and detecting the output field of the last stripline resonator, one can spectroscopically probe the properties of the system in the driven dissipative regime. We calculate the stationary polariton density and density–density correlations g (2) for the last cavity, which can be measured via the output field. Our results display a transition from a coherent to a quantum field as the ratio of on-site interactions to driving strength is increased.
Arrays of circuit cavities offer fascinating perspectives for exploring quantum many-body systems in a driven dissipative regime where excitation losses are continuously compensated by coherent input drives. Here we investigate a system consisting of three transmission line resonators, where the two outer ones are driven by coherent input sources and the central resonator interacts with a superconducting qubit. Whereas a low excitation number regime of such a device has been considered previously with a numerical integration, we here specifically address the high excitation density regime. We present analytical approximations to these regimes in the form of two methods. The first method is a Bogoliubov or linear expansion in quantum fluctuations which can be understood as an approximation for weak nonlinearities. As the second method we introduce a combination of mean-field decoupling for the photon tunneling with an exact approach to a driven Kerr nonlinearity which can be understood as an approximation for low tunneling rates. In contrast to the low excitation regime we find that for high excitation numbers the anti-bunching of output photons from the central cavity does not monotonously disappear as the tunnel coupling between the resonators is increased.
The Bose-Hubbard model (BHM) describes bosons hopping across sites and interacting on-site. Inspired by the success of BHM simulators with atoms in optical lattices, proposals for implementing the BHM with photons in coupled nonlinear cavities have recently emerged. Two coupled semiconductor microcavities constitute a model system where the hopping, interaction and decay of exciton polaritons-mixed light-matter quasiparticles-can be engineered in combination with site-selective coherent driving to implement the driven-dissipative two-site optical BHM. Here we explore the interplay of interference and nonlinearity in this system, in a regime where three distinct density profiles can be observed under identical driving conditions. We demonstrate how the phase acquired by polaritons hopping between cavities can be controlled through polariton-polariton interactions. Our results open new perspectives for synthesizing density-dependent gauge fields using polaritons in two-dimensional multicavity systems.
One of the most studied model systems in quantum optics is a two-level atom strongly coupled to a single mode of the electromagnetic field stored in a cavity, a research field named cavity quantum electrodynamics or CQED. CQED has recently received renewed attention due to its implementation with superconducting artificial atoms and coplanar resonators in the so-called circuit quantum electrodynamics (cQED) architecture. In cQED, the couplings can be much stronger than in CQED due to the design flexibility of superconducting circuits and to the enhanced field confinement in one-dimensional cavities. This enabled the realization of fundamental quantum physics and quantum information processing experiments with a degree of control comparable to that obtained in CQED. The purpose of this chapter is to investigate the situation where the resonator to which the atom is coupled is made nonlinear with a Kerr-type nonlinearity, causing its energy levels to be nonequidistant. The system is then described by a nonlinear Jaynes-Cummings Hamiltonian. This considerably enriches the physics since a pumped nonlinear resonator displays bistability, parametric amplification, and squeezing. The interplay of strong coupling and these nonlinear effects constitutes a novel model system for quantum optics that can be implemented experimentally with superconducting circuits. This chapter is organized as follows. In a first section we present the system consisting of a superconducting Kerr nonlinear resonator strongly coupled to a transmon qubit. In the second section, we describe the response of the sole nonlinear resonator to an external drive. In the third section, we show how the resonator bistability can be used to perform a high-fidelity readout of the transmon qubit. In the last section, we investigate the quantum backaction exerted by the intracavity field on the qubit.
Superconducting circuits constitute a promising platform for future implementation of quantum processors and simulators. Arrays of capacitively coupled transmon qubits naturally implement the Bose-Hubbard model with attractive on-site interaction. The spectrum of such many-body systems is characterized by low-energy localized states defining the lattice analog of bright solitons. Here, we demonstrate that these bright solitons can be pinned in the system, and we find that a soliton moves while maintaining its shape. Its velocity obeys a scaling law in terms of the combined interaction and number of constituent bosons. In contrast, the source-to-drain transport of photons through the array occurs through extended states that have higher energy compared to the bright soliton. For weak coupling between the source or drain and the array, the populations of the source and drain oscillate in time; for chains of even length, their population remains low at all times, while it can reach half the number of total bosons in odd chains. Implications of our results for actual experimental realizations are discussed.
A superconducting qubit coupled to a readout resonator is currently the building block of multiple quantum computing as well as quantum optics experiments. A typical qubit-resonator system is coupled in the dispersive regime, where the detuning between qubit and resonator is much greater than the coupling between them. In this work, we fabricated and measured a superconducting transmon-resonator system in the nondispersive regime. The dressed states formed by the mixing of the bare qubit and resonator states can be further mixed by applying a drive on the qubit, leading to the formation of polariton states. We report experimental studies of transitions between polariton states at varying driving powers and frequencies and show how the nondispersive coupling of the higher levels of the qubit-resonator system modifies the polariton eigenstates and the corresponding transition frequencies. We also report close agreement with numerical results obtained from a driven Jaynes-Cummings model beyond the dispersive regime.
The coherent light-matter interaction at the single-photon and electronic qubit level promises to be a remarkable potential for nonclassical information processing. Besides the efforts of improving the figure of merit of the cavities, here we demonstrate strong anharmonicity in the polariton dressed states via dark state resonances in a highly dissipative cavity. It is shown that the vacuum Rabi oscillation occurs for a single quantum emitter inside a cavity even with the bosonic decay-to-interaction rate ratio exceeding 102{10}^{2}102, when the photon field is coupled to an auxiliary high-QQQ cavity. Moreover, photon blockade is observable in such a highly dissipative cavity quantum electrodynamics system. This study provides a promising platform for overcoming decoherence and advancing the coherent manipulation of polariton qubits.