[Paper Review] Controlling a diatomic shape resonance with non-resonant light

Ruzin Ağanoğlu, Mikhail Lemeshko+3 more|arXiv (Cornell University)|May 4, 2011

Cold Atom Physics and Bose-Einstein Condensates4 references3 citations

TL;DR

This paper proposes using non-resonant laser light to shift the energy of a diatomic shape resonance toward the temperature of a trapped ultracold atomic ensemble, enhancing the thermal population of short-range atom pairs. By exploiting the anisotropic polarizability of atom pairs, the method increases the pair density by up to two orders of magnitude—10× for 87Rb at 100 μK and 100× for 88Sr at 20 μK—enabling more efficient photoassociation through dynamic or static control schemes.

ABSTRACT

A (diatomic) shape resonance is a metastable state of a pair of colliding atoms quasi-bound by the centrifugal barrier imposed by the angular momentum involved in the collision. The temporary trapping of the atoms' scattering wavefunction corresponds to an enhanced atom pair density at low interatomic separations. This leads to larger overlap of the wavefunctions involved in a molecule formation process such as photoassociation, rendering the process more efficient. However, for an ensemble of atoms, the atom pair density will only be enhanced if the energy of the resonance comes close to the temperature of the atomic ensemble. Herein we explore the possibility of controlling the energy of a shape resonance by shifting it toward the temperature of atoms confined in a trap. The shifts are imparted by the interaction of non-resonant light with the anisotropic polarizability of the atom pair, which affects both the centrifugal barrier and the pair's rotational and vibrational levels. We find that at laser intensities of up to $5 imes 10^{9}$ W/cm$^2$ the pair density is increased by one order of magnitude for $^{87}$Rb atoms at $100 μ$K and by two orders of magnitude for $^{88}$Sr atoms at $20 μ$K.

Motivation & Objective

• To enhance the efficiency of photoassociation in ultracold atomic gases by increasing the thermal population of atom pairs at short interatomic distances.
• To overcome the limitation that shape resonances in ultracold systems are typically too high in energy to be significantly populated at typical trap temperatures.
• To develop a method for actively controlling the energetic position of a shape resonance without relying on resonant light or specific atomic level structures.
• To enable coherent control of binary reactions by making shape resonances tunable via non-resonant laser fields.
• To explore both dynamic and static schemes for implementing resonance control in experimental setups using picosecond pulses or constant fields.

Proposed method

• Model the interaction of non-resonant light with the anisotropic polarizability of a diatomic atom pair, which shifts the centrifugal barrier and alters the rovibrational energy levels.
• Use a 1D effective potential model to describe the shape resonance in the presence of a non-resonant laser field, treating the field as a perturbation that modifies the effective potential barrier.
• Calculate the thermally averaged pair density as a function of laser intensity and field frequency, assuming the system reaches thermal equilibrium under the modified potential.
• Investigate both dynamic and static control schemes: in the dynamic scheme, a long non-resonant laser pulse adiabatically shifts the resonance energy; in the static scheme, a constant field is applied to establish a new equilibrium distribution.
• Apply a short probe pulse (e.g., picosecond) to detect the enhanced pair density at short distances, ensuring it is fast compared to rotational and translational dynamics.
• Account for avoided crossings between overlapping resonances (e.g., J=4 and J=8 in 88Sr) in the presence of strong fields, requiring a 2D treatment of rovibrational motion beyond 1D approximations.

Experimental results

Research questions

• RQ1 Can the energy of a diatomic shape resonance be shifted toward the trap temperature using non-resonant light to enhance the thermal population of short-range atom pairs?
• RQ2 How does the anisotropic polarizability of a diatomic pair mediate the shift of a shape resonance under non-resonant laser irradiation?
• RQ3 What is the maximum enhancement in thermally averaged pair density achievable for different atomic species (e.g., 87Rb and 88Sr) at experimentally feasible laser intensities?
• RQ4 Under what conditions can adiabatic following of the resonance by a non-resonant laser pulse be achieved, and how does this affect the feasibility of dynamic control?
• RQ5 Can a static non-resonant field be used to pre-condition the atomic cloud to maximize the pair density for subsequent photoassociation?

Key findings

• Non-resonant laser light with intensities up to 5×10⁹ W/cm² increases the thermally averaged pair density by a factor of 10 for 87Rb atoms at 100 μK.
• For 88Sr atoms at 20 μK, the same laser intensity enhances the pair density by a factor of 100, demonstrating a two-order-of-magnitude improvement.
• The enhancement is maximized when the laser-induced shift aligns the shape resonance energy with the trap temperature, indicating optimal control conditions.
• Adiabatic following of the resonance by a long non-resonant pulse is not feasible for 87Rb due to its rotational period (~2 μs) being longer than the resonance lifetime (~100 ns), limiting dynamic control efficiency.
• For 88Sr, with a shorter rotational period (~350 ns) and longer lifetime (~500 ns), adiabatic control is more feasible, supporting the potential for dynamic enhancement.
• In systems with multiple overlapping resonances, such as J=4 and J=8 in 88Sr, strong laser fields induce avoided crossings, transferring some of the narrow resonance character to broader resonances and increasing their lifetime and contribution to the pair density.