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arXiv:1201.3388 · New Journal of Physics

Photon condensation in circuit quantum electrodynamics by engineered dissipation

D Marcos, Andrea Tomadin, Sebastian Diehl, Peter Rabl

Published May 1, 2012• 72 citations
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Abstract

We study photon condensation phenomena in a driven and dissipative array of superconducting microwave resonators.Specifically, we show that by using an appropriately designed coupling of microwave photons to superconducting qubits, an effective dissipative mechanism can be engineered, which scatters photons towards low-momentum states while conserving their number.This mimics a tunable coupling of bosons to a low-temperature bath, and leads to the formation of a stationary photon condensate in the presence of losses and under continuous-driving conditions.In this paper, we propose a realistic experimental setup to observe this effect in two or multiple coupled cavities, and study the characteristics of such an out-of-equilibrium condensate, which arise from the competition between pumping and dissipation processes.

DOI
10.1088/1367-2630/14/5/055005

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We study photon condensation phenomena in a driven and dissipative array of superconducting microwave resonators.Specifically, we show that by using an appropriately designed coupling of microwave photons to superconducting qubits, an effective dissipative mechanism can be engineered, which scatters photons towards low-momentum states while conserving their number.This mimics a tunable coupling of bosons to a low-temperature bath, and leads to the formation of a stationary photon condensate in the presence of losses and under continuous-driving conditions.In this paper, we propose a realistic experimental setup to observe this effect in two or multiple coupled cavities, and study the characteristics of such an out-of-equilibrium condensate, which arise from the competition between pumping and dissipation processes.
We present a scheme for the dissipative preparation of an entangled steady state of two superconducting qubits in a circuit quantum electrodynamics (QED) setup. Combining resonator photon loss---a dissipative process already present in the setup---with an effective two-photon microwave drive, we engineer an effective decay mechanism which prepares a maximally entangled state of the two qubits. This state is then maintained as the steady state of the driven, dissipative evolution. The performance of the dissipative state preparation protocol is studied analytically and verified numerically. In view of the experimental implementation of the presented scheme we investigate the effects of potential experimental imperfections and show that our scheme is robust to small deviations in the parameters. We find that high fidelities with the target state can be achieved both with state-of-the-art three-dimensional, as well as with the more commonly used two-dimensional transmons. The promising results of our study thus open a route for the demonstration of a highly entangled steady state in circuit QED.
Abstract The seminal phenomenon of the Bose-Einstein condensation has been observed on a large variety of physical platforms, e.g., superfluid helium, fermions with attractive interactions, quasiparticles in solids, and ultracold atomic gases. Recently, the Bose–Einstein condensation of non-interacting photons in an optical microcavity has been confirmed experimentally. Here, we report the experimental observation of Bose-Einstein like condensation and collective Bogoliubov excitations in a low dissipative microwave resonator with embedded superconducting quantum network composed of multiple flux qubits. Under strong coherent pumping the resonator mode becomes macroscopically populated, giving rise to hybridized photon–qubit collective modes. The Bogoliubov-like collective excitations appearing in a response to a nearby-frequency probe tone, accompanied by pronounced bistability and hysteresis in the measured transmission coefficient, provide the first experimental evidence of a Bose–Einstein–like condensate of microwave photons on a superconducting circuit platform. A theoretical framework based on Gross-Pitaevskii formalism and taking into account the ac Stark effect inducing the effective interaction between photons, quantitatively reproduces the experimental observations and identifies the regime of appearance of microwave Bogoliubov excitations. These results establish a proof of principle for exploiting driven collective states in superconducting circuits as a platform for quantum-limited microwave detection and engineered many-body photonic systems for quantum information processing.
Superconducting circuits are a powerful platform for studying and controlling the interaction between light and matter at the quantum level. In these systems, superconducting qubits act as artificial atoms (with matter-like degrees of freedom), whereas microwave resonators play the role of oscillators hosting photons (with photonic-like degrees of freedom). A major advantage of this platform is the ability to tailor the electromagnetic environment to which the qubits are coupled. This degree of control makes it possible to realize well-known quantum optics models, like the Jaynes-Cummings model, as well as more complex systems, like quantum electrodynamics close to a bandgap. In this thesis, we engineer structured electromagnetic environments and couple superconducting qubits to them to experimentally study their interaction. By coupling multiple microwave resonators together, we create a metamaterial. When an atom interacts with the metamaterial, an atom-photon bound state emerges. We observe the dynamics of the creation and dissolution of the atom-photon bound state, as well as the spectral content of its photonic component, for the first time to our knowledge.Our metamaterial is intrinsically nonlinear because each resonator is formed by an array of Josephson junctions to serve as an inductor. When the system is pumped, its phase diagram exhibits multimode dissipative phase transitions with timescales on the order of hundred seconds. There is ongoing theoretical debate about whether such phase transitions can occur in one-dimensional systems, a question we address and resolve in this work.Furthermore, we engineer qubit decay using two different approaches. In the first one, we engineer the decay of two coupled atoms to two waveguides by using a symmetric–antisymmetric coupling configuration. This approach enables selective coupling to bright and dark states of the system. In the second one, we suppress the Purcell decay of a qubit using a compact lumped-element Purcell filter. In addition, we characterize the Purcell decay by employing an auxiliary superconducting qubit as a sensitive power detector directly coupled to the feedline waveguide used for the qubit readout.In summary, this thesis presents three different methods for controlling light–matter interactions in structured quantum systems, including decay suppression with both Purcell filters and symmetry-selective couplings. The thesis also introduces new experimental techniques for probing atom-photon bound states and provides direct evidence of collective phenomena in driven-dissipative quantum metamaterials.
We present a superconducting circuit device that provides active, on-demand, tunable dissipation on a target mode of the electromagnetic field. Our device is based on a tunable “dissipator” that can be made lossy when tuned into resonance with a broadband filter mode. When driven parametrically, this dissipator induces loss on any mode coupled to it with energy detuning equal to the drive frequency. We demonstrate the use of this device to reset a superconducting qubit’s readout cavity after a measurement, removing photons with a characteristic rate greater than 50μs−1 . We also demonstrate that the dissipation can be driven constantly to simultaneously damp and cool the cavity, effectively eliminating thermal photon fluctuations as a relevant decoherence channel. Our results demonstrate the utility of our device as a modular tool for environmental engineering and entropy removal in circuit quantum electrodynamics. Published by the American Physical Society 2024
We present an experimental feasible scheme to synthesize two-mode continuous-variable entangled states of two superconducting resonators that are interconnected by two gap-tunable superconducting qubits. We show that, with each artificial atom suitably driven by a bichromatic microwave field to induce sidebands in the qubit-resonator coupling, the stationary state of the photon fields in the two resonators can be cooled and steered into a two-mode squeezed vacuum state via a dissipative quantum dynamical process, while the superconducting qubits remain in their ground states. In this scheme the qubit decay plays a positive role and can help drive the system to the target state, which thus converts a detrimental source of noise into a resource.
In microwave quantum optics, dissipation usually corresponds to quantum jumps, where photons are lost one by one. Here we demonstrate a new approach to dissipation engineering. By coupling a high impedance microwave resonator to a tunnel junction, we use the photoassisted tunneling of quasiparticles as a tunable dissipative process. We are able to adjust the minimum number of lost photons per tunneling event to be one, two or more, through a dc voltage. Consequently, different Fock states of the resonator experience different loss processes. Causality then implies that each state experiences a different energy (Lamb) shift, as confirmed experimentally. This photoassisted tunneling process is analogous to a photoelectric effect, which requires a quantum description of light to be quantitatively understood. This work opens up new possibilities for quantum state manipulation in superconducting circuits, which do not rely on the Josephson effect.