Topological Winding and Unwinding in Metastable Bose-Einstein Condensates

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field level, the transition is accompanied by formation of gray solitons, or density notches, which serve as an experimental signature of this phenomenon.

Figure 1

Amplitude (solid curves with the left reference), and phase (dotted curves with the right reference) of metastable states of the GPE for $g_{1\mathrm{D}}N=0.6\pi$. Uniform solutions with different values of the phase winding (i) $J=1$, and (vi) $J=0$ are smoothly connected through the broken-symmetry gray soliton (ii)–(v) with a self-induced phase slip at $\Omega =0.5$.

Figure 2

(a) Energy difference between the metastable plane-wave and soliton states. The soliton solutions exist in the area surrounded by two phase boundaries (white dotted curves). (b) Corresponding angular momentum. The soliton solutions make it possible to smoothly connect quantized integer values of average angular momentum.

Figure 3

(a) The lowest energy of the Hamiltonian for each angular-momentum subspace for $N=40$, $g_{1\mathrm{D}}=2\pi \times 7.5\times {10}^{-3}$. (b) Enlargement of (a) near the critical point. Densely packed blue curves are spectra within $L\in \{0,N\}$. Otherwise the spectra are sparse. (c) Two-body correlation function of eigenstates for each angular-momentum subspace. (d) Expectation value of the angular momentum of each eigenstate, in the presence of symmetry-breaking potential $\widehat{V}$ as a function of $\Omega$.