Spectrum of the Dicke model in a superconducting qubit-oscillator system

Abstract

We calculate the transmission spectrum of a superconducting circuit realization of the Dicke model and identify spectroscopic features that can serve as signatures of the superradiant phase. In particular, we calculate the resonance frequencies of the system as functions of the bias term, which is usually absent in studies on the Dicke model but is commonly present in superconducting qubit circuits. To avoid over-complicating the proposed circuit, we assume a fixed coupling strength. This situation precludes the possibility of observing signatures of the phase transition by varying the coupling strength across the critical point. We show that the spectrum obtained by varying the bias point under fixed coupling strength can contain signatures of the normal and superradiant phases: in the normal phase one expects to observe two spectral lines, while in the superradiant phase four spectral lines are expected to exist close to the qubits' symmetry point. Provided that parameter fluctuations and decoherence rates are sufficiently small, the four spectral lines should be observable and can serve as a signature of the superradiant phase.

Hidden symmetry in the biased Dicke model

“…In this work, we found the -condition for the hidden Z 2 symmetry in the biased Dicke model H Nq (8) and determined the explicit expression (17) for the corresponding symmetry operator J Nq . This was achieved by using the ansatz (11) based on our recent results for the AQRM [23]. We proved that the J Nq operator commutes with the Hamiltonian H Nq (8) and has a quadratic relation (22) in terms of H Nq , thereby establishing the existence of Z 2 symmetry within the biased Dicke model.…”

“…Finally, we note that the ansatz (11) works surprisingly well, it not only leads to the J operators for the biased Dicke model, but is also capable of providing solutions for other AQRM-related models. For example, we have also used this ansatz to determine the J operators for the anisotropic AQRM and the asymmetric Rabi-Stark model [35].…”

“…As a result of using superconducting circuits, circuit QED is capable of realising the Dicke model with much larger light-matter coupling strengths g/ω close to or even larger than 1 [8][9][10]. In addition, there is a natural generalisation of the Dicke model to the biased Dicke model by introducing biased superconducting flux qubits [11]. These biases are experimentally easy to vary and are deeply related to the system properties.…”

Hidden symmetry in the biased Dicke model

“…As a result of using superconducting circuits, circuit QED is capable of realising the Dicke model with much larger light-matter coupling strengths g/ω close to or even larger than 1 [7,8,9]. In addition, there is a natural generalisation of the Dicke model to the biased Dicke model by introducing biased superconducting flux qubits [10]. These biases are experimentally easy to vary and are deeply related to the system properties.…”

Finite-system Multicriticality at the Superradiant Quantum Phase Transition

“…Instead of entering the large-size limit, a finite-size system may also undergo a quantum phase transition (QPT) if the thermodynamic limit can be reached in an alternative way. This is the case of the Dicke model [18][19][20][21][22][23][24][25][26][27][28][29][30], which describes a bosonic mode collectively coupled to multiple qubits. In this model, a second-order QPT appears when the ratio of the mode frequency to the qubit transition frequency approaches zero [31][32][33].…”