# Resonating valence bonds and spinon pairing in the Dicke model

### Submission summary

 As Contributors: R. Ganesh Arxiv Link: http://arxiv.org/abs/1803.03267v1 (pdf) Date submitted: 2018-04-03 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

See full Ontology or Topics database.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

#### Published as SciPost Phys. 4, 044 (2018)

Resubmission 1803.03267v2 on 13 June 2018

Submission 1803.03267v1 on 3 April 2018

## Reports on this Submission

### Anonymous Report 2 on 2018-6-5 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1803.03267v1, delivered 2018-06-05, doi: 10.21468/SciPost.Report.490

### Strengths

1. It present a novel scheme of detecting RVB physics using an optical setup.

2. It present a rigorous mathematical analysis of the phenomenon in the context of the experimental setup.

### Weaknesses

1. The paper makes a set of assumptions which would make experimental realizations of the theory tricky.

### Report

The paper proposes a novel scheme for realizing RVB state using optical (lossy cavity) setup. The paper is well written and easy to understand and I would recommend publication of the following changes are made ( see below)

### Requested changes

1. One needs a clear discussion supplemented by explicit numbers about the assumptions. For example, the assumptions are listed in the paper. Form each of these, it would be nice to have numerical estaimate of several experimental parameters which could refklect the possibility of exterimental validity of the assumtpion.

2. Coudl the author elaborate a bit more, at a qualitative level, as to what happens to the realization of spinon physics in case each of the assumtpions are relaxed. When would one expect the effect that they want to see go away?

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: good

### Report 1 by Indrani Bose on 2018-6-3 (Invited Report)

• Cite as: Indrani Bose, Report on arXiv:1803.03267v1, delivered 2018-06-03, doi: 10.21468/SciPost.Report.486

### Strengths

1. Proposes a novel scheme to synthesize resonating valence bond (RVB) states using the Dicke Hamiltonian.
2. Simulation protocol suggested of spinon-doping in cavity QED experiment.

### Weaknesses

1. The paper is interesting with no specific weakness.

### Report

The RVB states are entangled many body wavefunctions which are of considerable relevance in understanding the physical properties of strongly correlated systems. In these states spin pairs form singlets. The proposal put forward by the Authors to synthesize RVB states in a cavity QED setup utilising the Dicke model of two-level atoms, represented as S =1/2 spins, coupled to a common photon mode is novel and of significant interest. A spinon-doped RVB state is obtained when a Stern-Gerlach measurement of emitted photons is made with the spinons representing unpaired spins. An analogue of a finite-sized superconductor is obtained in the form of a mixed state with fluctuating spinon pairs under non-measurement of photons. The protocol when extended to large system sizes demonstrates a quantum phase transition in the open Dicke model. The proposal of using the Dicke system to synthesize RVB states has advantages over solid state and cold atom experiments.

### Requested changes

None.

• validity: good
• significance: high
• originality: high
• clarity: ok
• formatting: good
• grammar: good