Quantum networks in divergence-free circuit QED

Parra-Rodriguez, A.; Rico, E.; Solano, E.; Egusquiza, I. L.

doi:10.1088/2058-9565/aab1ba

Cited by 50 publications

(70 citation statements)

References 46 publications

(173 reference statements)

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“…This equation is central for experimentally tailoring a bosonic environment, relating the effective impedance to the resulting spectral density J(ω). It has also been shown recently that the parallel contribution C int in the spectral density is indeed an essential quantity for a consistent description of such systems in all parameter regimes [64,65].…”

Section: A Spectral Density and The System-bath Interactionmentioning

confidence: 91%

“…III D, we show the derivation of the Kondo parameter α. The approach we use is based on a linear circuit analysis, but the results can also be derived by an exact Lagrangian quantization [60][61][62][63][64][65]. In addition, we provide also a consistency check based on the Born-Markov approach, in Sec.…”

Section: Implementation Of the Spin-boson Model With A Microwavementioning

confidence: 99%

“…Guidelines for a determination of the spectral density in open circuits is given in Appendix A as well as in other Refs. [60][61][62][63][64][65] Voltage fluctuations across the impedance are described by the operatorV . The exact circuit diagram of the considered setup is shown in Fig.…”

Section: A Spectral Density and The System-bath Interactionmentioning

confidence: 99%

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Quantum simulation of the spin-boson model with a microwave circuit

et al. 2018

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We consider superconducting circuits for the purpose of simulating the spin-boson model. The spin-boson model consists of a single two-level system coupled to bosonic modes. In most cases, the model is considered in a limit where the bosonic modes are sufficiently dense to form a continuous spectral bath. A very well known case is the ohmic bath, where the density of states grows linearly with the frequency. In the limit of weak coupling or large temperature, this problem can be solved numerically. If the coupling is strong, the bosonic modes can become sufficiently excited to make a classical simulation impossible. Here, we discuss how a quantum simulation of this problem can be performed by coupling a superconducting qubit to a set of microwave resonators. We demonstrate a possible implementation of a continuous spectral bath with individual bath resonators coupling strongly to the qubit. Applying a microwave drive scheme potentially allows us to access the strongcoupling regime of the spin-boson model. We discuss how the resulting spin relaxation dynamics with different initialization conditions can be probed by standard qubit-readout techniques from circuit quantum electrodynamics.

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Section: A Spectral Density and The System-bath Interactionmentioning

confidence: 91%

Section: Implementation Of the Spin-boson Model With A Microwavementioning

confidence: 99%

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Quantum simulation of the spin-boson model with a microwave circuit

et al. 2018

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“…Let us assume that the qubits have total capacitances (shunt plus intrinsic junction capacitance) C 1 and respectively C 2 . In the weak coupling limit

C_{L}, C_{R} ≪ C_{1}, C_{2}

, using standard quantum network analysis in the presence of dissipation, [ 112 ] we obtain the Hamiltonian Equation (1). Here the resistor plays the role of a thermal bath with an Ohmic spectral density proportional to the resistance R .…”

Section: An Experimental Proposal To Test Our Findingsmentioning

confidence: 99%

Bath‐Induced Collective Phenomena on Superconducting Qubits: Synchronization, Subradiance, and Entanglement Generation

et al. 2021

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A common environment acting on a pair of qubits gives rise to a plethora of different phenomena, such as the generation of qubit–qubit entanglement, quantum synchronization, and subradiance. Here, time‐independent figures of merit for entanglement generation, quantum synchronization, and subradiance are defined, and an extensive analytical and numerical study of their dependence on model parameters is performed. A recently proposed measure of the collectiveness of the dynamics driven by the bath is also addressed, and it is found that it almost perfectly witnesses the behavior of entanglement generation. The results show that synchronization and subradiance can be employed as reliable local signatures of an entangling common‐bath in a general scenario. Finally, an experimental implementation of the model based on two transmon qubits capacitively coupled to a common resistor is proposed, which provides a versatile quantum simulation platform of the open system in any regime.

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“…We use the gauge degree of freedom to find an optimal gauge such that the results of the effective model are as close as possible to full model. Importantly, we take account of the need for a multimode description [13][14][15][16] in the quest for achieving the ultra-strong coupling regime [17][18][19][20]. To increase the flexibility, we not only consider the extremal cases of purely flux or charge mediated coupling but perform a general gauge transformation that smoothly interpolates between the two.…”

mentioning

confidence: 99%

Optimal gauge for the multimode Rabi model in circuit QED

Roth

Hassler

DiVincenzo

2019

Phys. Rev. Research

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In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are not necessarily the preferred options in the case of multiple resonator modes.Circuit QED [1, 2] is a central subject of quantum information science that has deepened our understanding of light-matter interaction [3][4][5]. Most implementations consist of a two-level system (qubit) that is coupled to a linear environment. The qubit is formed by the two lowest energy levels of an anharmonic multilevel-system. For the physics of interest only the qubit subspace is important. The Schrieffer-Wolff (SW) transformation [6,7] is the standard method to perturbatively derive an effective Hamiltonian description within this subspace. For most purposes, it is sufficient to consider the effective Hamiltonian only to first order, yielding the well known quantum Rabi model (QRM). However, since the Hamiltonian of the non-truncated system is unique only up to a unitary transformation, the effective description is gauge dependent to every finite order [8,9]. This gauge ambiguity becomes particularly important in the (ultra) strong coupling regime. It has been found that the QRM derived in a gauge where the qubit-resonator coupling is mediated by the flux variables leads to different predictions than the one where the coupling is mediated by the charge variables [10][11][12].In this work, we look at the issue from a different perspective. We use the gauge degree of freedom to find an optimal gauge such that the results of the effective model are as close as possible to full model. Importantly, we take account of the need for a multimode description [13][14][15][16] in the quest for achieving the ultra-strong coupling regime [17][18][19][20]. To increase the flexibility, we not only consider the extremal cases of purely flux or charge mediated coupling but perform a general gauge transformation that smoothly interpolates between the two. A similar transformation has been used in [21] to extend the Jaynes-Cummings model into the ultra-strong coupling regime.We find that already the second order term of the effective Hamiltonian within the SW method is a good indicator of the validity of the QRM. Based on this observation, we derive a simple analytical criterion for the optimal gauge and benchmark it against numerical sim- FIG. 1. (a) Circuit diagram of a qubit with potential U (φq), capacitance Cq, and inductance Lq that is coupled to a general reactive environment. In the Forster form, the latter is represented by N resonators with capacitance...

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Quantum networks in divergence-free circuit QED

Cited by 50 publications

References 46 publications

Quantum simulation of the spin-boson model with a microwave circuit

Quantum simulation of the spin-boson model with a microwave circuit

Bath‐Induced Collective Phenomena on Superconducting Qubits: Synchronization, Subradiance, and Entanglement Generation

Optimal gauge for the multimode Rabi model in circuit QED

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