Observation of modulation-induced Feshbach resonance

Abstract

In this work, we observe a novel resonant mechanism, namely the modulation-induced Feshbach resonance. By applying a far-detuned laser to the cesium D2 transition with intensity modulation, we periodically shake the energy levels of atomic collisional states. This periodic shaking connects the free-scattering states to shallow molecular states. At specific frequencies, we observe significant atom loss, which corresponds to the resonant coupling between these two types of states. This precisely corresponds to a form of Feshbach resonance, yet in the frequency domain rather than the magnetic-field domain. Using this method, we can directly scan the energy spectrum of molecular bound states without synthesizing any molecules. In addition to these bound states, we can also probe the molecular states embedded in the continuum, which are typically very difficult to detect by the conventional methods based on molecular synthesis. Moreover, by using a far-detuned laser instead of a magnetic field coil, it enables spatially dependent control over atomic interactions, coupling multiple levels simultaneously, and inducing new Feshbach resonances for those atoms that do not have conventional magnetic resonances. Therefore, we believe that this new resonant mechanism offers new opportunities for controlling atomic and molecular interactions in quantum simulations.

Figures (4)

• Figure 1: (a) Experimental setup. A Bose-Einstein condensate with approximately $10^5$ cesium atoms, trapped by a light sheet plus a cross-dipole trap in the $x$-$y$ plane, is prepared in the hyperfine state of $|F=3,m_F=3\rangle$ with a magnetic field applied along the $z$ axis. A 23-GHz-detuned light is sent along the $z$ axis with a left-hand circular polarization as depicted in panel (b). This light has an intensity modulation with a modulation frequency $\omega$, which oscillates the differential energy shift between atomic collisional states and couples the free-scattering states to the molecular states such as $4g(4)$ in panel (c).
• Figure 2: Typical atom loss signals in the frequency domain and dependence of the resonance position shift on the average peak intensity. (a)-(c) The relative atom number $N_m/N_0$ versus the modulation frequency $\omega$ after 5 ms exposure to 0.86 W/cm$^2$ (average peak intensity) modulation light at 18.59 G, 18.66 G and 18.70 G, respectively. The resonant peaks are labelled with corresponding molecular states $6g6$ and $6s$ in panels (a) and (c), while these two molecular states are strongly mixed in panel (b). The experimental atom loss signal (dark solid circle) in each panel is fitted with a Fano profile (red solid lines), and all error bars represents one standard deviation of measurements. In panel (d), a linear fitting example of the resonance position shift caused by the DC light intensity for $4g(4)$, $4d$ molecular states and one of the $6s$-$6g(6)$ mixed molecular states at respective magnetic field of 17.27 G, 47.36 G and 18.66 G, is presented, which offers a route to compensate the resonance frequency shift.
• Figure 3: Multiple resonances of the $4g(4)$ molecular state. (a) Resonances in the frequency domain at 19.41G. (b) Atom-loss feature as a function of the magnetic field under a fixed modulation frequency of 150 kHz. The average peak intensity of applied modulation light is 0.87 W/cm$^2$ in both two panels.
• Figure 4: The energy spectrum of cesium molecular states. The filled (unfilled) symbols in the plot represent molecular bound states data (molecular states in the continuum) below (above) the atomic scattering threshold that corresponds to the black solid line along $\omega=0$. The other solid lines are the theoretical models calculated for molecular states $6g(6)$, $6s$, $4g(4)$ and $4d$. The main plots near 20 G (a) and 48 G (b) depict the energy of $4g(4)$, $6s$ and $4d$, exhibiting obvious dependence on magnetic field. In the inset (c), an avoid crossing between the $6s$ state and the near-frequency-independent $6g(6)$ state is shown. This feature is not plotted in (a) as it's a narrow span near 18.66 G. The $4g(4)$ and $4d$ data are obtained at a average peak intensity of 0.86 W/cm$^2$ and compared with theoretical lines shifted from their original Feshbach resonance points to the optically shifted ones measured in experiments, while the $6s$ and $6g6$ data are obtained by varying the average peak intensity and compensating the DC component of the light shift by linear fitting.