Generating resonating-valence-bond states through Dicke subradiance

Abstract

Dicke's original thought experiment with two spins (two-level atoms) coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to many spins as a way to synthesize highly entangled states. We suggest a protocol in which we start with a direct product state of M atoms in the excited state and N atoms in the ground state, placed within a lossy cavity. A null observation for photon emission collapses the system onto a dark state which, remarkably, has resonating valence bond (RVB) character. We demonstrate this by taking advantage of the symmetry of the initial state under permutations of the M excited atoms and of the N unexcited atoms. Using angular momentum analysis, we reexpress the wavefunction of the dark state to illustrate its RVB character. We discuss two limiting cases in detail, with M = 1 (one excited atom) and M = N (equal number of excited and unexcited atoms). In the latter case, we show that the probability for null emission scales as N −1 making it possible to generate highly entangled RVB states of 20 spins or more.

Directional Dicke Subradiance with Nonclassical and Classical Light Sources

“…For more than two two-level atoms the subradiant Dicke states are merely non-symmetric [1]; the corresponding states have been recently used to form a unimodular basis [24,25]. Various theoretical investigations have discussed the preparation [26][27][28][29][30][31][32][33][34][35][36][37][38][39] as well as the subradiant emission characteristics of non-symmetric Dicke states for larger atomic ensembles, either using a semiclassical theory [28,[33][34][35][36][37][38][39] or within a full quantum mechanical treatment [13,[30][31][32]. Very recently, the first experimental observation of retarded subradiant spontaneous decay for more than two emitters has been reported [40].…”

Resonating valence bonds and spinon pairing in the Dicke model

“…When no photon is observed, the collapsed wavefunction is an RVB state with S tot = 0 containing M dimers and no unpaired spins. This 'strong' RVB state was discussed in our earlier work [20] where a similar protocol was proposed to isolate subradiant (non-emitting) states. Here, we have extended this idea to non-zero emission, showing that a positive detection of photons also leads to an RVB state.…”

“…To obtain this form, we have used the powerful constraint of in-row permutation symmetry. This forces each row wavefunction to have the maximal possible S tot value [20]. + p. Using known expressions for Clebsch Gordan coefficients [24], we obtain E λ as…”

“…We assume that spins are initialized in a direct product state as in Refs. [19,20], with M spins in the excited state and N spins in the ground state. This can be written as…”

“…Under well-known conditions [19,20], the spin-photon system is described by the Dicke Hamiltonian within the rotating wave approximation (or more precisely, the Tavis Cummings Hamiltonian),…”