Implementation of the Dicke Lattice Model in Hybrid Quantum System Arrays

Abstract

Generalized Dicke models can be implemented in hybrid quantum systems built from ensembles of nitrogen-vacancy (NV) centers in diamond coupled to superconducting microwave cavities. By engineering cavity assisted Raman transitions between two spin states of the NV defect, a fully tunable model for collective light-matter interactions in the ultra-strong coupling limit can be obtained. Our analysis of the resulting non-equilibrium phases for a single cavity and for coupled cavity arrays shows that different superradiant phase transitions can be observed using existing experimental technologies, even in the presence of large inhomogeneous broadening of the spin ensemble. The phase diagram of the Dicke lattice model displays distinct features induced by dissipation, which can serve as a genuine experimental signature for phase transitions in driven open quantum systems.PACS numbers: 42.50. Pq, 05.30.Rt, The Dicke model (DM) [1] was first introduced to describe the collective coupling of N two-level atoms to a single optical mode, and has developed into a prototype model for collective quantum phenomena in atomic and solid-state systems [2]. Most prominently, the DM predicts a superradiant phase transition (SRT) [3][4][5] when the collective atom-field coupling reaches the ultra-strong coupling regime and becomes comparable to the optical and atomic frequencies. While the existence of this transition for atoms coupled directly to an optical mode is subject of ongoing debates [6][7][8][9][10], effective DMs can be implemented, for example, using tailored Raman couplings in driven cold-atom systems [11][12][13][14][15][16]. In these systems, the non-equilibrium SRT [11,17] has recently been observed [18][19][20], which represents an important step towards more detailed investigations of phase transitions in open quantum systems. Yet a true many-body generalization of these models with multiple independent atomic and optical degrees of freedom [21][22][23][24][25][26] still faces considerable experimental and theoretical challenges.In this work we describe a new approach for realizing generalized DMs, by using atomic [27], molecular [28] or solid-state spin ensembles [29][30][31] coupled to superconducting microwave cavities [see Fig. 1 a)]. Such hybrid quantum systems [32,33] have originally been proposed for quantum information processing applications, and strong collective interactions between microwave photons and solid-state spin ensembles have already been observed [34][35][36][37][38][39][40]. Compared to optical or all superconducting circuit realizations [41][42][43], the current approach allows us to combine large ensembles of (almost) identical spins with high-quality microwave resonators that can be easily coupled together to form large arrays [44]. For the example of nitrogen-vacancy (NV) spin ensembles in diamond, we describe the implementation of effective light-matter interactions in the ultra-strong coupling regime and evaluate the resulting non-equilibrium phases for a single spin ensemble and for co...

Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons

“…Another possible application is in inversion-invariant systems consisting of arrays of (pseudo)spins with large angular momentum such as in Refs. [17,41,42], where fluctuations above the mean-field treatment are diagonalized by Bogoliubov theory.…”

Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model

“…This is the case for the quantum Rabi model [35,36], which corresponds to a single-qubit DM. Furthermore, the engineering of effective Hamiltonians allows to implement generalized quantum optical models [37,38], including anisotropic couplings or two-photon interactions. In the case of anisotropic couplings, reaching the USC regime leads to parity-symmetry breaking [39,40] and to a rich phase diagram in the many-body limit [41].…”

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

“…Quenches across a non-equilibrium phase transition provide further insight into the interplay between noise and external drives on criticality and thermalization [7,8]. In this context photonic systems play a prominent role, thanks to their versatility [9][10][11][12][13][14][15].…”