Observation of Microwave Shielding of Ultracold Molecules
Loïc Anderegg, Sean Burchesky, Yicheng Bao, Scarlett S. Yu, Tijs Karman, Eunmi Chae, Kang-Kuen Ni, Wolfgang Ketterle, John M. Doyle
HHarnessing the potential wide-ranging quantum science applications of moleculeswill require control of their interactions. Here, we use microwave radiation todirectly engineer and tune the interaction potentials between ultracold cal-cium monofluoride (CaF) molecules. By merging two optical tweezers, eachcontaining a single molecule, we probe collisions in three dimensions. Thecorrect combination of microwave frequency and power creates an effectiverepulsive shield, which suppresses the inelastic loss rate by a factor of six, inagreement with theoretical calculations. The demonstrated microwave shield-ing shows a general route to the creation of long-lived, dense samples of ultra-cold molecules and evaporative cooling. a r X i v : . [ phy s i c s . a t o m - ph ] F e b bservation of Microwave Shielding of UltracoldMolecules Lo¨ıc Anderegg, , Sean Burchesky, , Yicheng Bao, , Scarlett S. Yu, , Tijs Karman, , Eunmi Chae, Kang-Kuen Ni, , , Wolfgang Ketterle, , John M. Doyle , Department of Physics, Harvard University, Cambridge, MA, USA Harvard-MIT Center for Ultracold Atoms, Cambridge, MA, USA ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Radboud University, Institute for Molecules and Materials,Heijendaalseweg 135, 6525 AJ Nijmegen, Netherlands Department of Physics, Korea University, Seongbuk-gu, Seoul, Republic of Korea Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
February 9, 2021
Applications of ultracold molecules in quantum simulation, precision measurement, ultra-cold chemistry, and quantum computation (
1, 2 ), have led to rapid progress in direct cooling( ), assembly ( ), trapping ( ), and control of molecules ( ). Engineering andcontrol of molecular interactions will enable or enhance many of these appliactions. In par-ticular, collisional interactions play a critical role in the ability to cool and, therefore, con-trol molecules. While there has been some success with sympathetic and evaporative cooling(
24, 25 ), these efforts have been hindered by large inelastic loss rates for both reactive and non-reactive molecular species in optical traps ( ). Suppressing these inelastic losses, and moregenerally tuning interactions, is key to effective evaporative cooling of ultracold molecules andquantum applications. 2 path to this is shielding, whereby molecules can be repelled from short range distanceswhere inelastic processes occur. Various shielding schemes for atoms ( ) and moleculeshave been proposed ( ). Recently, a scheme using DC electric fields to generate repulsiveinteractions was demonstrated in a 2D geometry for KRb molecules ( ). Here, we reportmicrowave shielding of Ca F molecules in three dimensions using optical tweezer traps.By tuning the microwave frequency from blue to red detuned, the system goes from shieldedto “anti-shielded”, changing the inelastic collision rate by a factor of 24, in agreement withtheoretical calculations.The microwave shielding mechanism studied here works as follows. Continuous, near res-onant microwave fields dress the molecular states, generating an oscillating dipole moment inthe CaF molecule that gives rise to strong, long-range dipolar interactions ( ). With the cor-rect microwave frequency, this interaction is repulsive. Additionally, the dipolar interactionsignificantly enhances the elastic collision rate resulting in a high elastic-to-inelastic collisionalratio, which is a key feature for evaporative cooling. In the microwave shielding scheme weuse, the uppermost dressed state adiabatically converts to the repulsive branch of the dipole-dipole interaction. This leads to a classical turning point at long range (
37, 38 ), as shown inFig. 1(a), preventing molecules from reaching short range where they would be lost with highprobability ( ). There will be residual inelastic loss at long range, predicted to be a resultof non-adiabatic transitions (so-called “microwave-induced loss”) (
37, 38 ). Coupled-channelcalculations have shown that effective shielding requires circular polarization and high Rabifrequencies of the microwave field ( ). Circular polarization provides coupling to the repul-sive branch of the resonant dipole-dipole interaction regardless of the orientation of the collisionaxis relative to the molecule orientation, resulting in shielding in the bulk, i.e. three dimensions.Rabi frequencies can be made high enough to create a large gap between field-dressed levels,ensuring adiabaticity during the collision. 3igure 1:
Microwave shielding overview (a) Diagram of the shielding process. The upperdressed state leads to a repulsive potential, preventing the molecules from reaching short rangeand undergoing loss. (b) CaF energy levels of the X Σ + electronic ground state showing theN=1 and N=0 rotational states separated by 20.5 GHz. The shielding transition is shown ingreen. The purple arrow shows the Landau-Zener sweep to the absolute ground state. (c)Experimental schematic showing the relative orientations of the helical antenna with respect tothe tweezers. The tweezer light is linearly polarized along the z axis, parallel to the magneticfield, B.Our experiment starts from a magneto-optical trap (MOT) of Ca F molecules ( ). Weuse Λ -enhanced grey molasses cooling to load molecules into a conservative 1064 nm opticaldipole trap (
17, 42 ). Single molecules are then transferred into two 780 nm optical tweezertraps ( ). The tweezers have a beam waist of about . µ m and a depth of . mK. Lightassisted collisions caused by the Λ -cooling light during tweezer loading ensures no more thana single molecule in each tweezer. As detailed previously ( ) the two tweezer traps can bemerged to create a colliding pair of molecules in a single trap. This is accomplished using asingle 780 nm laser source to create one stationary trap, and using an acousto-optical deflector(AOD), one steerable trap. The light for theses two traps is combined, then focused down,forming two tightly focused tweezer traps that can be merged. We measure a typical moleculetemperature of ∼ µ K ( ), both before and after merging. The molecules occupy many spatialmodes therefore the collisions are three-dimensional in nature.4igure 2: Microwave shielding of CaF collisions
The grey trace (10.8 ms) shows the bare twobody loss of unshielded ground state collisions. The blue trace (64 ms) shows the shielded lossrate at a Rabi frequency of 23 MHz, and magnetic field of 27 G while blue detuned. The redtrace (2.7 ms) shows the loss rate while red detuned with a Rabi frequency of 20 MHz, andmagnetic field of 27 G.Once the tweezers are loaded, we apply an optical pumping pulse to populate the | N =1 , J = 1 / , F = 0 , m f = 0 (cid:105) state (Fig. 1(b)). Next, we use a Landau-Zener microwavesweep to move the population to the absolute ground state | N = 0 , J = 1 / , F = 0 , m f = 0 (cid:105) .This transition is nominally dipole forbidden but an applied 4 Gauss magnetic field mixes inthe | N = 0 , F = 1 , m f = 0 (cid:105) state, providing a significant transition dipole moment. To removeany remaining population in the N=1 rotational level, we apply a 5 ms pulse of resonant light,heating the N=1 molecules out of the tweezer trap. The two molecules, both in the groundinternal state, are then merged together into a single tweezer for collisions to take place. At thispoint, the shielding is turned on for a variable amount of time before the tweezers are separated,and the molecules are transferred back to the N=1 manifold for imaging.Circularly polarized microwaves are generated by a × helical antenna array ( ), Fig.1(c). The helical antennas are designed for axial mode operation, creating circular polarization5ith a helicity set by the winding of the antenna. An array is used to increase the cleanli-ness of the circular polarization and the overall output power. The 20.5 GHz microwaves aregenerated from mixing a low phase noise 18.5 GHz source with a 2 GHz source locked to alow noise oscillator ( ). The 20.5 GHz signal is then amplified and split into four paths ofequal length through phase stable cables. Each antenna has a separate 5 W microwave ampli-fier and a mechanical phase shifter. The microwaves propagate into a stainless-steel vacuumchamber through a glass window along the z-axis, defined as the direction of the magnetic field,Fig. 1(c). We determine the polarization of the microwave field by measuring the Rabi fre-quency of the σ + , σ − , and π transitions between the states | N = 1 , J = 1 / , F = 0 , m f = 0 (cid:105) and | N = 0 , J = 1 / , F = 1 , m f = ± , (cid:105) . Accounting for the magnetic field dependent ma-trix elements, the σ + and σ − field components indicate the degree of circular polarization in theplane transverse to the axial magnetic field, while the π component of the field is related to thetilt angle of the polarization ellipse relative to the z-axis. Using the measured Rabi frequencies,we then adjust the phases of the four individual antennas to maximize the target circular fieldcomponent, while minimizing the other two polarizations. The helical antenna array generatesclean circular polarization in free space, however the reflections from metal components in andaround the vacuum chamber degrade the polarization cleanliness to a power ratio of right- toleft-handed circular polarization of 100 ( ).To create collisional shielding, we use the | N = 1 , J = 1 / , F = 1 , m f (cid:105) hyperfine mani-fold, with an applied 27 Gauss magnetic field. The magnetic field direction is such that theupper state in the manifold | N = 1 , J = 1 / , F = 1 , m f = − (cid:105) is driven by the high purity cir-cular polarization. After merging the tweezers, we prepare the upper dressed state by switchingon low power microwaves with a frequency a few MHz blue detuned of | N = 1 , J = 1 / , F =1 , m f = − (cid:105) . Then, adiabatically, the amplitude of the microwaves is ramped to full powerin ∼ µ s. Using the highest energy m f level ensures that the upper dressed state does not6igure 3: Theory (a) Rate coefficient versus Rabi frequency. Both shielding (blue) and anti-shielding (red) are shown. The elastic rate is shown in yellow. The solid lines are resultswithout including spin, the circles include spin. (b) Plot of loss versus microwave ellipticityangle, ξ ( ), for a Rabi frequency of 23 MHz. The tweezer trap’s tensor AC Stark shift is thedominant factor reducing the effective degree of shielding. The elastic rate is nearly unaffectedby the AC Stark shift and magnetic field.cross any other levels as the microwave power is ramped up. The lifetime of the single-particledressed state in the optical tweezer is limited by the phase noise of the microwave source to > ms.The collisional lifetime of the bare ground state is the reference for our shielding perfor-mance comparison. We measure the trap frequency and temperature of the bare ground statemolecules to be the same as molecules prepared in the upper dressed state, thus ensuring thatthe density of microwave dressed molecules and bare ground state molecules are comparable.The ratio of the measured lifetimes is thus the ratio of the 2-body loss rates.At a Rabi frequency of 23 MHz, and dressing 3 MHz blue detuned from the | N = 0 , F =0 , m f = 0 (cid:105) to | N = 1 , J = 1 / , F = 1 , m f = − (cid:105) transition in a 27 Gauss field, as in Fig. 2,the shielded lifetime was 64 ms ( β = 7 . . × − cm /s), six times longer than the bareground state lifetime of 10.8 ms ( β = 4 . . × − cm /s). The ratio of the lifetimes are inagreement with a coupled channel loss rate calculation, Fig. 3. We find experimentally that theshielded lifetime is relatively independent of the polarization purity from
100 : 1 to
10 : 1 in7ower at a Rabi frequency of ∼ MHz.While the upper dressed state produces a repulsive shielding potential, the lower dressedstate adiabatically connects to the attractive branch of the dipole-dipole interaction as the moleculesapproach during the collision, causing anti-shielding (
37, 38 ). Guided by this theory, we pre-pare the lower dressed state by flipping the direction of the magnetic field, which effectivelyswaps the handedness of the microwaves such that the lowest m f level ( | N = 1 , J = 1 / , F =1 , m f = +1 (cid:105) ) is now the one being driven most strongly by the circularly polarized microwaves.We prepare the lower dressed state with a microwave power ramp, with the microwaves MHzred detuned. We measure this anti-shielded lifetime to be . ms ( β = 1 . . × − cm /s),or a factor of about four faster than the bare ground state and a factor of twenty-four faster thanthe shielded state, see Fig. 2.We use coupled-channel methods to calculate microwave shielding of CaF molecules. Simi-lar to previous work ( ), the colliding molecules are modeled as rigid rotors interacting throughdipole-dipole interactions and with external magnetic and microwave fields. For details see ( ).In contrast to previous studies, we include the tensor AC Stark shift caused by the intensetweezer light. At short range, a fully absorbing boundary condition is imposed that yieldsuniversal loss in the absence of microwave dressing. Non-adiabatic transitions between dressedstates lead to microwave-induced loss, whereby the microwave Rabi frequency is converted intokinetic energy. Short-range losses occur to a lesser extent as the potentials involved are mainlyrepulsive. The results of two sets of calculations are shown in Fig. 3. First, shown in Fig. 3(a),we assume the microwave polarization is perfectly circular about the magnetic field and tweezerpolarization directions. Cylindrical symmetry is exploited to expedite the calculations. Second,shown in Fig. 3(b), the ellipticity of the microwave polarization is added, breaking cylindricalsymmetry, which makes the computations more demanding such that explicitly accounting for(hyper)fine structure becomes intractable. Hence, we make the approximation of treating spin8mplicitly by an enhanced rotational g -factor and test the accuracy of this approximation inFig. 3(a), see ( ) for a detailed discussion.Previous theoretical work on microwave shielding (
37, 38 ) indicated a strong dependenceon the polarization. The tensor Stark shift due to the optical tweezer light aligns the moleculeswhich competes with the resonant dipolar interactions that lead to shielding. The coupled chan-nel calculations performed here indicate this limits shielding for perfectly circular polarizationbut reduces the sensitivity to polarization imperfections, see Fig. 3(b). The | N = 1 , J =1 / , F = 1 , m f (cid:105) hyperfine manifold, used for shielding, has a significant tensor polarizabil-ity ( ). The tweezer in which the collisions take place is linearly polarized along the z-axis,parallel to the magnetic field and perpendicular to the plane containing the polarization ellipseof the microwaves. At a tweezer trap depth of 1.8 mK for the ground state and no applied mag-netic field, we observe a splitting of 10 MHz between the m f = 0 and m f = ± states. Thistensor Stark shift is the dominant limiting factor of the observed shielding process.It has been shown previously ( ) that the CaF( Σ ) fine structure can limit the effectivenessof microwave shielding, leading to losses enhanced by orders of magnitude compared to calcula-tions neglecting (hyper)fine structure or to Σ bialkali molecules, with much weaker hyperfineinteractions. Here, we use the | N = 0 , J = 1 / , F = 0 (cid:105) → | N = 1 , J = 1 / , F = 1 (cid:105) transi-tion, see Fig. 1(a), to achieve shielding. At low magnetic fields, the electron and nuclear spinsin these states are approximately coupled to a total spin singlet, which effectively eliminatesthe fine structure couplings. As shown in Fig. 4(a), our calculations predict an enhancement ofthe shielding at low magnetic field but only in the absence of tensor AC Stark shifts. Includingtensor AC Stark shifts, this interaction dominates the loss at low magnetic field, and the inter-play between these two effects results in only a weak magnetic field dependence, see ( ) for adetailed discussion. This is in agreement with experimentally observed shielding lifetimes thatare similar for 10 Gauss, 27 Gauss, and 54 Gauss, Fig. 4(a).9igure 4: Dependence of shielding on microwave power and magnetic field
The shieldingfactor is the ratio of the bare loss rate to the measured loss rate. (a) Shielding factor versusmagnetic field at a Rabi frequency of 23 MHz. We find the effect of shielding to be robustover this range of magnetic fields, a result of the tensor AC Stark shift from the trap light. (b)Shielding factor versus Rabi frequency. We find the crossover point where shielding beginsto be around 3 MHz. The experimental data is taken at 27 G while the theory curve does notinclude the effect of spin.As predicted from theory, the shielding effect shows a clear power dependence, Fig. 4(b).The loss rate increases from β = 7 . . × − cm /s to β = 2 . . × − cm /s whenthe microwave power is reduced from to MHz of Rabi frequency on the σ − transition,while keeping the polarization unchanged. Decreasing the power further to . MHz of Rabifrequency, we measure an increased loss rate of β = 5 . . × − cm /s, slightly higherthan the bare ground state. The losses measured are almost entirely from long-range microwavedriven non-adiabatic transitions, therefore the bare ground state loss rate is not a lower bound(
37, 38 ). As the gap between the upper dressed state providing the repulsive potential and thelower dressed state decreases, the loss rate at low Rabi frequency is faster than the bare groundstate loss rate.In conclusion, we demonstrate microwave shielding of inelastic collisions in three dimen-sions with ultracold CaF molecules in an optical tweezer trap. The relative ratios of experi-10entally measured 2-body lifetimes agree well with results of coupled channel calculations andthe qualitative features of shielding theory. By blue detuning the microwaves, we observe afactor of six suppression of inelastic loss in the shielded upper dressed state, relative to the bareground state. By red detuning, we create an anti-shielded lower dressed state, leading to anenhanced loss rate. This shielding mechanism may be extended to a wide range of molecules,including polyatomic molecules (
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