# Resonating valence bonds and spinon pairing in the Dicke model

### Submission summary

 As Contributors: R. Ganesh Arxiv Link: https://arxiv.org/abs/1803.03267v2 (pdf) Date accepted: 2018-06-19 Date submitted: 2018-06-13 02:00 Submitted by: Ganesh, R. Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms (with states $\vert 0 \rangle$ and $\vert 1 \rangle$) coupled to a common photon mode. In the lossy cavity limit, starting with an initial state of $M$ atoms excited and $N$ atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets of the form $\frac{1}{\sqrt{2}}[\vert 0 1 \rangle - \vert 1 0 \rangle]$. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or `spinons'. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to a mixed quantum state with a fluctuating number of spinon pairs -- an inchoate superconductor. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization ($M-N$), the emission exhibits a continuous transition from a dark state to a bright state. This is reflected in the spinon pair number distribution which can be tuned from sub-poissonian to super-poissonian regimes. This opens an exciting route to simulate RVB states and superconductivity.

### Ontology / Topics

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Published as SciPost Phys. 4, 044 (2018)

We thank the referees for their comments and the editor for the recommendation. In line with the comments sought by Referee 2, we have included some parameters from a suitable experimental setup. We believe that the modified manuscript makes a more convincing case for the viability of our proposals.

We are happy to see that the first referee has recommended publication as is. The second referee finds our work to be novel and well written. He/she has raised two questions which are important from the point of view of achieving an experimental realization. We ourselves have been thinking about these questions for some time.

The first question is about numerical estimates to support the assumptions made in our work. In the revised manuscript, we have included experimental parameters from Mlynek et al. (2014), an experimental study of two superconducting qubits in a microwave cavity. The most important assumption in our work is the ‘lossy cavity’ limit. These parameters show that the lossy-cavity limit is indeed experimentally realisable. In addition, the numbers also justify the use of the rotating wave approximation. We have modified the final section (Summary and Discussion) to discuss these parameters and their relevance.

For other assumptions in our work, it is not easy to obtain numerical estimates. For example, we are not aware of any experiments which have estimated the spin-spin interaction energy scale within a lossy-cavity setup. Such quantities are highly sensitive to details of the experimental setup and cannot be generically estimated. If an experimental lab were to take up our proposals, we believe they can make straightforward consistency checks to see if our assumptions are satisfied (e.g., the fidelity with which a singlet dark state is obtained in a two spin system).

In the second question, the referee asks about the consequences that arise when our assumptions are violated. As the referee has noted, the manuscript clearly lays out its assumptions. Weak violations of assumptions will lead to weak deviations in results, e.g., the probabilities for emission of different photon numbers could be altered by small amounts. In the manuscript, we have speculated that spin-spin interactions (neglected in our approach) could bring about a qualitative change to induce coherent Cooper pairing. We also have speculated that these effects can lead to a preference for shorter dimers. A more precise discussion is beyond the scope of the manuscript as there are a large number of possibilities. We hope to soon present a quantitative analysis, broadly discussing the experimental viability of our proposal. For instance, we hope to provide estimates for emission-time, a quantity that is central to one of our assumptions. For the sake of brevity, we believe it is best to keep this manuscript at the level of a theoretical proposal that is rigorous as long as the stated assumptions are obeyed.

We hope to convince the referee (and readers) that our manuscript proposes new directions, and will motivate further theoretical and experimental work.

### List of changes

We have made several minor changes for grammar and for clarity.

We have included a new paragraph ('With a suitable experimental system such as...') in the 'Summary and Discussion' section. This provides parameters from an experimental paper -- we argue that the realized setup is favourable for our proposals.