Creation and manipulation of bound states in the continuum with lasers: Applications to cold atoms and molecules

We show theoretically that it is possible to create and manipulate a pair of bound states in the continuum in ultracold atoms by two lasers in the presence of a magnetically tunable Feshbach resonance. These bound states are formed due to coherent superposition of two electronically excited molecular bound states and a quasibound state in the ground-state potential. These superposition states are decoupled from the continuum of two-atom collisional states. Hence, in the absence of other damping processes they are nondecaying. We analyze in detail the physical conditions that can lead to the formation of such states in cold collisions between atoms and discuss the possible experimental signatures of such states. An extremely narrow and asymmetric shape with a distinct minimum of the photoassociative absorption spectrum or the scattering cross section as a function of collision energy will indicate the occurrence of a bound state in the continuum (BIC). We prove that the minimum will occur at the energy at which the BIC is formed. We discuss how a BIC will be useful for efficient the creation of Feshbach molecules and manipulation of cold collisions. Experimental realizations of BIC will pave the way for a new kind of bound-bound spectroscopy in ultracold atoms.

Figure 1

A schematic diagram for creating a BIC in ultracold atoms. Two lasers, $L_1$ and $L_2$, are used to excite PA transitions from the magnetic Feshbach-resonant collisional state of two ultracold ground-state ($S+S$) atoms to the two bound states, $b_1$ and $b_2$, respectively, in the same electronically excited molecular potential. The magnetic Feshbach resonance is considered to be a two-channel model in the electronic ground-state potentials, with the lower channel being open and the upper one being closed. In the large separation limit the ground-state channel potential corresponds to two separated $S+S$ atoms, while the excited-state potential corresponds to two separated $S+P$ atoms.

Figure 2

Dimensionless spectrum $S_1\left(E\right)E_f$ as a function of $E/E_f$ (where $E_f=\hslash {\Gamma }_f/2$) for $g_1=0.25$ (solid curve), $g_1=0.5$ (dashed curve), and $g_1=0.75$ (dash-dotted curve), with $q_{1f}=-0.5$, $q_{2f}=-1.0$, $g_2=2.0$, ${\tilde{\delta }}_2=-0.5$, and ${\tilde{\delta }}_1=1.5$. For the solid curve the three complex eigenvalues of ${\tilde{H}}_{\mathrm{eff}}$ are ${\tilde{E}}_1=1.0964-0.0010i$, ${\tilde{E}}_2=1.4989-0.0992i$, and ${\tilde{E}}_3=-1.5953-3.1498i$; for the dashed curve ${\tilde{E}}_1=1.0242-0.0164i$, ${\tilde{E}}_2=1.4862-0.1653i$, and ${\tilde{E}}_3=-1.5104-3.3184i$; for the dash-dotted curve ${\tilde{E}}_1=0.9581-0.0421i$, ${\tilde{E}}_2=1.4645-0.2111i$, and ${\tilde{E}}_3=-1.4226-3.4968i$. When $g_1=0.1803$, ${\tilde{E}}_1$ becomes real and is equal to 1.1180, which corresponds to the minimum of the spectral lines. The spike height of the solid curve is $2.2\times {10}^4$.

Figure 3

The same as Fig. 2, but for $g_1=5.5$ (solid curve), $g_1=5.0$ (dashed curve), and $g_1=4.5$ (dash-dotted curve) with fixed parameters $q_{1f}=0.5$, $q_{2f}=1.0$, $g_2=5.0$, ${\tilde{\delta }}_1=1.45$, and ${\tilde{\delta }}_2=-1.5$. For the solid curve the eigenvalues are ${\tilde{E}}_1=0.6645-4.5\times {10}^{-6}i$, ${\tilde{E}}_2=-2.2178-0.4279i$, and ${\tilde{E}}_3=1.55338-11.0720i$; for the dashed curve ${\tilde{E}}_1=0.7036-0.0002i$, ${\tilde{E}}_2=-2.2165-0.44027i$, and ${\tilde{E}}_3=1.51292-10.5595i$; for the dashed-dotted curve ${\tilde{E}}_1=0.7466-0.0008i$, ${\tilde{E}}_2=-2.2153-0.4534i$, and ${\tilde{E}}_3=1.4687-10.0457i$. For $g_1=5.2516$, ${\tilde{E}}_1$ is real and is equal to 0.6583. The spike height of the solid curve is $1.0\times {10}^6$.