Rydberg-Induced Solitons: Three-Dimensional Self-Trapping of Matter Waves

We propose a scheme for the creation of stable three-dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatiotemporal “light bullets.” Off-resonant dressing to Rydberg $nD$ states is shown to provide nonlocal attractive interactions, leading to self-trapping of mesoscopic atomic clouds by a collective excitation of a Rydberg atom pair. We present detailed potential calculations and demonstrate the existence of stable solitons under realistic experimental conditions by means of numerical simulations.

Figure 1

(a) Simplified level scheme of the considered Rydberg-dressing approach. The off-resonant coupling of condensed ground state ($|g⟩$) atoms to strongly interacting Rydberg states ($|e⟩$) gives rise to a stable bright soliton bound by a rim of a collective quantum excitation of a Rydberg atom pair, shown in (b). Depicted is a numerically obtained soliton formed by dressing a Rb condensate to $65D_{3/2}$ Rydberg states with a Rabi frequency $\Omega /2\pi =0.5\mathrm{MHz}$ and laser detuning $\Delta /2\pi =32\mathrm{MHz}$. Shown are half-maximum isodensity surfaces of the BEC (inner red sphere) and the Rydberg-pair density (outer blue shell), while the gray scale gives the interior density.

Figure 2

(a) Existence curves for stable (thick solid lines) and unstable (dotted lines) solitons for several $\eta =\gamma /\alpha$ and typical length scales of modulational instability (thin blue lines) (b) Corresponding parameter regions for self-trapping. The dots show numerical results using the potential Eq. (5) for a Rb condensate with atom numbers $N=1000$, 3000, 4850.

Figure 3

(a) Two atom level scheme for dressing to $65D_{3/2}$ Rydberg states and Rydberg interactions $V_{\beta }^{\mathrm{Ryd}}(r)$. (b) Resulting single potential curve (${\tilde{m}}_J=3/2$) for $\vartheta =0$ according to Eq. (5). (c) Attractive and repulsive branches of interaction strengths $C_6^{(\beta )}$ vs $n$. For $n\ge 59$, all curves are attractive.

Figure 4

Effective ground-state potentials [(c),(d)] resulting from two-photon $n{D}_{3/2}$ state dressing [(a),(b)] to ${\tilde{m}}_J=3/2$ [(a),(c)] and ${\tilde{m}}_J=1/2$ [(b),(d)] Rydberg states, with a two-photon Rabi frequency $\Omega /2\pi =({\Omega }_1{\Omega }_2/2\delta )/2\pi =0.5\mathrm{MHz}$ and laser detuning $\Delta /2\pi =32\mathrm{MHz}$. The aspect ratio of the resulting soliton is shown in (e) as a function of $\Omega$ for ${\tilde{m}}_J=3/2$ (circles) and ${\tilde{m}}_J=1/2$ (squares). The insets in (e) show respective 3D soliton profiles [cf. Fig. 1b] for $\Omega /2\pi =0.3\mathrm{MHz}$ and 0.5 MHz.

Figure 5

Self-trapped condensate dynamics after instantaneous turn-on of the dressing lasers and sudden release from a harmonic trap (${\omega }_{\mathrm{tr}}=170\mathrm{Hz}$). The white lines give the width of a freely expanding BEC. $65D_{3/2}$ Rydberg states are coupled with $\Omega /2\pi =0.5\mathrm{MHz}$ and $\Delta /2\pi =32\mathrm{MHz}$.