Disorder-Driven Density and Spin Self-Ordering of a Bose-Einstein Condensate in a Cavity

Farokh Mivehvar, Francesco Piazza, Helmut Ritsch
2017 Physical Review Letters  
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_2 symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative
more » ... se of the two condensate wavefunctions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially-averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
doi:10.1103/physrevlett.119.063602 pmid:28949625 fatcat:qyziwamak5apro5iitreqtnfh4