SciPost Phys. 4, 044 (2018) ·
published 30 June 2018

· pdf
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 twolevel 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 longranged 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 ($MN$), 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 subpoissonian to
superpoissonian regimes. This opens an exciting route to simulate RVB states
and superconductivity.