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 coupled to a common photon mode. In the lossy cavity limit, starting with an initial state with MM atoms excited and NN 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. 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 an inchoate superconductor – mixed quantum state with a fluctuating number of spinon pairs. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization, the emission exhibits a continuous transition from a dark state to a bright state. This opens an exciting route to simulate RVB states and superconductivity.
Highlights
4.1 Relative probabilities for photon emission 4.2 Tuning the imbalance in the initial state 4.3 Photon distribution in the thermodynamic limit 4.4 Consequences for superconductivity
We proposed a protocol to generate dark Resonating valence bond (RVB) states by a null-measurement for photon emission [20]
We demonstrated that the measurement of emission collapses the spin wavefunction into an RVB state with (N − M + 2p) = M (α − 1 + 2γ) unpaired spins
Summary
Resonating Valence Bond (RVB) states were originally proposed by Pauling in the context of benzene [1]. RVB theory [3, 4] postulates that the undoped cuprates, which are Mott insulators, have an analogous RVB ground state, viz., a superposition of all possible ways to cover the square lattice with singlet dimers This is an incompressible liquid of singlets, e.g., we cannot introduce additional singlets into this state. In lattice-RVB systems, an exciting line of investigation has been the response to an applied magnetic field This is a simpler proposition than conventional doping as it changes the number of singlets without introducing charge dynamics. The third result is a phase transition in the emission properties of the Dicke model which can be used to bring the system closer to superconductivity
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