Observation of Rydberg Blockade Due to the Charge-Dipole Interaction between an Atom and a Polar Molecule

Observation of Rydberg Blockade Due to the Charge-Dipole Interaction between an Atom and a Polar Molecule Alexander Guttridge ,1,2 Daniel K. Ruttley ,1,2 Archie C. Baldock ,1Rosario González-F´erez ,3 H. R. Sadeghpour ,4C. S. Adams ,1,2,* and Simon L. Cornish 1,2,† 1Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom 2Joint Quantum Centre Durham-Newcastle, Durham University, South Road, Durham, DH1 3LE, United Kingdom 3Instituto Carlos I de Física Teórica y Computacional, and Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain 4ITAMP, Center for Astrophysics | Harvard & Smithsonian, Cambridge, Massachusetts 02138, USA (Received 10 March 2023; accepted 15 May 2023; published 7 July 2023) We demonstrate Rydberg blockade due to the charge-dipole interaction between a single Rb atom and a single RbCs molecule confined in optical tweezers. The molecule is formed by magnetoassociation of a Rb þCs atom pair and subsequently transferred to the rovibrational ground state with an efficiency of 91(1)%. Species-specific tweezers are used to control the separation between the atom and molecule. The charge-dipole interaction causes blockade of the transition to the Rb(52s) Rydberg state, when the atommolecule separation is set to 310(40) nm. The observed excitation dynamics are in good agreement with simulations using calculated interaction potentials. Our results open up the prospect of a hybrid platform where quantum information is transferred between individually trapped molecules using Rydberg atoms. DOI: 10.1103/PhysRevLett.131.013401 Ultracold dipolar systems, such as Rydberg atoms and polar molecules, are promising platforms for quantum simulation and computation [1–14]. Rydberg atoms exhibit strong, long-range interactions that can be exploited to engineer quantum entanglement and multiqubit gates [12,15–20]. This approach exploits the Rydberg blockade mechanism, where strong van der Waals interactions between neighboring Rydberg atoms prevent simultaneous excitation of multiple atoms within a certain radius. Ultracold polar molecules also exhibit long-range interactions and possess a rich manifold of long-lived rotational states which can be coupled using microwave fields [21–23] to realize high-fidelity quantum operations [24–29]. Recent advances in optical tweezer arrays of Rydberg atoms [10–13] and ultracold molecules [30–35] provide the foundation to develop hybrid atom-molecule systems. A hybrid system composed of polar molecules and Rydberg atoms trapped in optical tweezer arrays offers a way to combine the advantages of both platforms. For example, quantum information can be encoded in the internal states of the molecule, and gates can be performed utilizing the strong interactions of Rydberg atoms [36–39]. This combines the fast high-fidelity interactions and readout possible with Rydberg atoms [20,40] with the long coherence times and lifetimes of polar molecules [21–23]. In addition, this hybrid system offers new capabilities, such as nondestructive readout of the molecular state [41–43], cooling of molecules using Rydberg atoms [44,45], and photoassociation of giant polyatomic Rydberg molecules [46–48]. Realizing controlled interactions between molecules and Rydberg atoms remains an outstanding challenge. These interactions extend beyond the van der Waals and dipoledipole interactions which have been widely used in single-species Rydberg systems [11] and the dipole-dipole interactions recently observed between polar molecules [49–52]. The long-range interaction of the Rydberg electron with the permanent dipole, d, of the polar molecule takes, in first order, the form of a charge-dipole interaction [46,53]. The interaction arises when the internal field due to the Rydberg electron and atomic core polarizes the molecular dipole, Vcdðr;RamÞ¼BN2−d·Fðr;RamÞ. Here ris the electron position, Ram is the dipole position with respect to the atomic core, and Nand Bare the quantum operators for molecular rotation and the associated rotational constant, respectively. The internal electric field is F¼eðr−RamÞ=jr−Ramj3þeRam=R3 am, leading to an anisotropic 1=R2 am interaction. For micron-scale separations, achievable in optical lattices and optical tweezers, these interactions are predicted to be strong enough to preclude the excitation of an atom to a Rydberg state in the presence of a molecule [36,37]. In this Letter, we demonstrate Rydberg blockade due to the charge-dipole interaction in a hybrid platform Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. PHYSICAL REVIEW LETTERS 131, 013401 (2023) Editors' Suggestion Featured in Physics 0031-9007=23=131(1)=013401(8) 013401-1 Published by the American Physical Society composed of a single 87Rb atom and a single 87Rb133Cs molecule confined in separate optical tweezers. The molecule is prepared in the rovibrational ground state using a combination of magnetoassociation and coherent optical transfer. We use species-specific optical tweezers to control the atom-molecule separation down to ∼300 nm without significant collisional loss. At this separation, we find that excitation of the Rb atom to a Rydberg state is suppressed. The adiabatic Hamiltonian for the hybrid Rydberg atommolecule system at large separations contains the charge induced-dipole interaction [46], and the S-wave scattering of the slow electron from the molecule [53–55]. The results described here hold for d<d cr ¼1.639 Debye [67], the Fermi-Teller critical dipole, to ensure that the electron only scatters from the molecule. The trapping potentials due to the optical tweezers and the effect of the magnetic field are neglected in the theoretical description. In Fig. 1(a), we show the resulting energy shift as a function of the separation Ram between a Rb atom in Rydberg state jri¼j52siand a RbCs molecule in the rovibrational ground state jGi¼jX1Σþ;v¼0;N ¼0i with d¼1.225 Debye [68] and B¼0.490 GHz [69]. Here, vand Nare the vibrational and rotational quantum numbers, respectively. At Ram ∼300 nm, we see the onset of a large shift arising from the charge-dipole interaction. The modulation in the energy arise from the oscillatory nature of the Rydberg electron wave function. For our choice of states the interaction is nonresonant and van der Waals interactions are ≃1kHz at these distances. Figure 1(b) shows the Rydberg electron density for our system with Ram ¼230 nm, highlighting the perturbation due to the polar molecule. The outermost minimum of the Rydberg electron wave function sets the range of interactions; this occurs at 220 nm for the state jri. The experimental geometry is shown in Fig. 1(c). The atom and molecule are prepared in species-specific tweezers. Both particles predominantly occupy the motional ground state of their respective traps. The tweezer separation, Rt, is set by controlling the relative tweezer alignment in all three spatial dimensions. The atom-molecule separation, Ram, is determined from the difference in the resulting potential minima. When the tweezers overlap, the atom-molecule separation is reduced compared to the tweezer separation (Ram <R t) due to the effect of each potential on the other species. For each measurement, we repeat an experimental sequence many times. Fluctuations in the relative alignment of the tweezers occur from shot to shot with an estimated standard deviation of 50 nm in each coordinate. Atomic fluorescence images are taken at the start and end of each sequence to determine the occupancy of each tweezer; molecules are detected by reversing the association procedure and imaging the resulting atom pair in separate tweezers. We apply various postselection criteria on the tweezer occupancies to obtain values and their associated confidence intervals from typically 200–1000 runs for different experimental scenarios [55]. Our experiments begin by loading single 87Rb and 133Cs atoms into species-specific optical tweezers [70]. After determining the trap occupations and performing rearrangement, the atoms are further cooled using Raman sideband cooling [71–73] and transferred to the hyperfine states jf¼1;m f¼1iRb þjf¼3;m f¼3iCs. To produce a molecule, we must prepare a Rb þCs atom pair in the ground state of relative motion in a single tweezer. We achieve this by merging a 817 nm tweezer containing a Rb atom into a 1065 nm tweezer containing a Cs atom. This protocol prepares a Rb þCs atom pair in the ground state of relative motion in 56(5)% of runs [73]. The electronic potential energy curves for RbCs are shown in Fig. 2(a). Weakly bound RbCs molecules in state jFiare formed using magnetoassociation on an interspecies Feshbach resonance at 197 G [35,74–76]. The magnetic field ramps used to associate and later dissociate the atom pair are shown in the upper panel of Fig. 2(b); the central panel shows the energy levels that these ramps navigate to access the state jFiat 181.6 G. The formation of weakly bound RbCs molecules is detected using pump-induced loss [55,77–79] which precludes atom-pair recovery when the association and merging steps are reversed [Fig. 2(b) lower panel]. We transfer the weakly bound molecule to the rovibrational ground state jGiusing two-photon stimulated Raman (a) (b) (c) FIG. 1. (a) Pair state energy shift as a function of the separation Ram between a Rb atom in state jri¼j52siand a RbCs molecule in state jGi¼jX1Σþ;v¼0;N ¼0i. The shaded region (shown inset) highlights the region relevant to the blockade measurements; the dashed line shows our best estimate of Ram and the range reflects the associated uncertainty. (b) A surface plot of the radial electron density of the Rydberg electron for Ram ¼230 nm. (c) Schematic of the experiment showing the atom and molecule trapped in species-specific optical tweezers separated along the yaxis. PHYSICAL REVIEW LETTERS 131, 013401 (2023) 013401-2 adiabatic passage (STIRAP) [80,81], as previously demonstrated for bulk gases of RbCs molecules [68,77,79,82]. In Fig. 2(c) we show the probability of recovering the atom pair after a round trip jFi→jGi→jFias a function of the single-photon detuning of either the pump or Stokes lasers, with the other laser held on single-photon resonance. When the Stokes laser is not resonant, the pump laser causes loss to other molecular states via the intermediate molecular state jEi¼j 3Π1;v 0¼29;J0¼1i. When the pump laser is far from resonant, the molecules remain in state jFi throughout the transfer sequence. In Fig. 2(d), we characterize the STIRAP efficiency using repeated transfers back and forth between states jFi and jGi. An odd number of successful one-way transfers results in the molecule occupying state jGi, whereas an even number returns it to state jFi. Only molecules that occupy state jFiat the end of the sequence are dissociated back into atom pairs for detection. The offset of the odd points indicates the combined efficiency of the cooling, merging, and magnetoassociation stages; in 50(1)% of runs we do not form a molecule, and thus reimage the atom pair independent of the STIRAP pulses. The maximum contrast between the odd and even points is limited primarily by the 35(5) ms lifetime of molecules in state jFiin the trap and the need to allow the magnetic field to stabilize before STIRAP [55]. We measure a one-way transfer efficiency of 91(1)%, consistent with the best reported efficiencies for RbCs in bulk gases [79,82]. To observe blockade, the charge-dipole interaction between the Rydberg atom and the molecule must be greater than the power-broadened transition linewidth. For our system, this is set by the Rabi frequency of 500(3) kHz; blockade therefore requires interactions shifts ≳1MHz. Our calculations in Fig. 1predict the atom-molecule distance must be below a blockade radius ∼300 nm to observe this effect, a distance smaller than the beam radii of the individual tweezers (∼1μm). We cannot achieve submicron separations by loading both species into the same tweezer, as the expected lifetime due to collisional loss is <1ms [83]. Instead we utilize species-specific tweezers at wavelengths of 1065 nm for the molecule and 817 nm for the atom. For the Rb atom, the ratio of polarizabilities for these wavelengths is αRb 817=αRb 1065 ∼6.3 [84], so that it is confined predominantly in the 817 nm tweezer (the “atom tweezer”). Conversely, for the RbCs molecule αRbCs 1065 =αRbCs 817 ∼4.5[85] so that it is confined predominantly in the 1065 nm tweezer (the “molecule tweezer”). Typical trap potentials are illustrated in the insets of Fig. 3. We investigate loss due to collisions between a Rb atom in state jgi¼j5s1=2;f ¼1;m f¼1iand a RbCs molecule by sweeping the position of the atom tweezer to a variable distance Rtfrom the molecule tweezer. The particles are held at this separation for 9.5 ms before the sweep is reversed and the particle survival probabilities are measured. The results are presented in Fig. 3. For the molecule, we report the atom-pair survival probability, postselected on cases where a weakly bound molecule was formed [55]. The upper panel shows the one-body survival probabilities from runs where either the Rb atom or the RbCs molecule FIG. 2. Formation of ground state RbCs molecules in optical tweezers. (a) Electronic potential curves for RbCs showing the pump and Stokes transitions that couple states jFi,jEi, and jGi. (b) Formation of weakly bound molecules by magnetoassociation of atom pairs using a Feshbach resonance at 197 G. The top panel shows the magnetic field ramps used to form molecules and then navigate the nearthreshold bound states shown in the middle panel. STIRAP is performed at 181.6 G when the molecule occupies the state jFi(indicated point). The lower panel shows the pump-induced loss of weakly bound molecules. The atom-pair survival probability P11 is measured after reversing the field ramp to dissociate any remaining molecules. (c) Atom-pair survival probability for a round trip jFi→jGi→jFi as a function of the one-photon detuning Δ1pof either the pump (from the transition jFi→jEi) or the Stokes (from the transition jEi→jGi) when the other laser is on resonance. (d) Repeated STIRAP transfers between states jFiand jGiwith a one-way efficiency of 91(1)%. The dashed lines show the experimental contrast; the shaded regions are the uncertainties. The inset shows the pulse profiles for a round-trip transfer. PHYSICAL REVIEW LETTERS 131, 013401 (2023) 013401-3 is present. The atomic survival probability is 97.2(4)%. For the molecule signal, we observe a survival probability of 48(2)%, primarily caused by loss prior to STIRAP due to the short lifetime of the state jFiin the trap. By compensating for the return STIRAP efficiency, we predict that a molecule in jGiis present in 53(3)% of runs in which a weakly bound molecule is created. The lower panel in Fig. 3shows the two-body survival probabilities for runs in which both an atom and a weakly bound molecule are initially prepared. When the tweezers are brought together, the wave functions of the particles begin to overlap and collisions cause loss of both the molecule and atom. We observe a reduction in the atom survival probability by 58(6)%, commensurate with the probability a molecule in state jGiis present. From a Gaussian fit we find the loss falls to 1=e2of its maximum value at Rt¼250ð20Þnm. To demonstrate blockade, we repeat the routine used to measure collisional loss, but use a shorter hold time of 3 ms when the tweezers are close together. Two-photon excitation of the Rb atom jgi→j6p3=2i→jriis performed during the hold time with the trapping light still present [55]. Atoms excited to state jriare antitrapped and ejected from the tweezers, mapping Rydberg excitation onto atom loss. To suppress collisional loss we hold the tweezers at a separation Rt¼420ð40Þnm, shown by the dotted line in Fig. 3. Here the error represents the systematic uncertainty from the alignment calibrations. As shown inset in Fig. 3, this equates to an atom-molecule separation of Ram ¼310ð40Þnm [55]. In Fig. 4, we demonstrate the blockade of the Rydberg transition of the Rb atom when a RbCs molecule in state jGiis present. Figure 4(a) shows the survival probability of the Rb atom as the Rydberg pulse duration is varied. For experimental runs where the molecule tweezer is empty (green circles), we observe Rabi oscillations between states jgiand jriwith a fitted frequency of 500(3) kHz. The observed damping is caused by laser frequency noise. In contrast, for runs where a molecule in state jGiis present (purple squares), we observe a suppression of the excitation to state jri. Here, the presence of the molecule shifts the energy of state jrithrough the charge-dipole interaction and thus blockades excitation during the Rydberg pulse. The frequency of the residual Rabi oscillations is almost identical to that for the unblockaded case. This is due to the sharp onset of the interaction shown in Fig. 1(a) combined with shot-to-shot variations in the relative alignment of the tweezers. For runs with the largest separations, the energy shift is smaller than the Rabi frequency of the Rydberg transition leading to a signal at the unshifted Rabi frequency. To simulate the expected excitation dynamics, we solve the Lindblad master equation [55]. We use the pair-state energy shifts shown in Fig. 1(a) to include a distancedependent energy shift. We account for the fact that the atom and molecule are predominantly prepared in the FIG. 3. Collisions between ground state RbCs molecules and Rb atoms held in separate species-specific optical tweezers. Particle survival probabilities are plotted as a function of the tweezer separation, Rt. For the molecule we report the atom-pair survival probability, post-selected on cases where a weakly bound molecule was formed [55]. Upper panel: experimental runs where either a single Rb atom (blue squares) or a single RbCs molecule (red circles) is present. Lower panel: runs where both the atom and the molecule are present. The dashed lines (and shaded regions) correspond to the mean values (and errors) from the onebody cases. The purple dotted line at Rt¼420 nm shows the tweezer separation for the measurement in Fig. 4(a). Insets: The potential energy of the atom (blue) and molecule (red) resulting from their own tweezer (dashed lines) and both tweezers (solid lines) for Rt¼2000 (left) and Rt¼420 nm (right). (a) (b) FIG. 4. (a) Survival probability of the Rb atom as a function of the Rydberg pulse duration for Ram ¼310ð40Þnm. Atoms excited to jriare ejected from the trap and lost. Events are postselected on the detection of a molecule in jGi(purple squares) or unsuccessful formation of a molecule (green circles). The solid lines show the results of simulations using the Lindblad master equation [55] using our estimated atom-molecule separation. (b) Rb atom survival probability as a function of the twophoton detuning, Δ, using a 1μs pulse for Ram ¼700ð40Þ(upper panel) and Ram ¼310ð40Þnm (lower panel). The detuning is defined relative to the transition center in the absence of a molecule. Symbols are as in (a) and solid lines show the results of simulations using the estimated atom-molecule separations. PHYSICAL REVIEW LETTERS 131, 013401 (2023) 013401-4 motional ground state of their respective tweezers by averaging the interaction over the ground-state wave function of relative motion. We also include experimental imperfections such as dephasing from laser frequency noise and shot-to-shot fluctuations in the relative alignment of the tweezers. Using our best estimates of the separation, we find good agreement between the results of the simulation and the experiment, as shown by the solid lines in Fig. 4(a). Figure 4(b) shows the effect of changing the atommolecule separation on the Rydberg blockade. In this experiment, we fix the pulse duration to approximate a πpulse and scan the two-photon detuning of the light driving the Rydberg transition. For Ram ¼700ð40Þnm, shown in the upper panel, the charge-dipole interaction is negligible. Here, the dominant interaction is van der Waals leading to a shift of ∼0.1kHz [86]. Consequently, the presence of a molecule does not affect the Rydberg excitation. However, for Ram ¼310ð40Þnm, shown in the lower panel, the presence of a molecule leads to an observed shift of the Rydberg transition to lower energy, as expected. The transition is significantly broadened due to the sensitivity of the charge-dipole interaction to the atommolecule separation. The broadening causes a concomitant reduction in the signal amplitude. Both these effects are reproduced by simulations using the same parameters as in Fig. 4(a) with the exception of the appearance of a shoulder in the lower panel of Fig. 4(b) which is highly sensitive to fluctuations in Ram. In conclusion, we have demonstrated blockade of the transition to the Rb(52s) Rydberg state due to the chargedipole interaction with a RbCs molecule in the rovibrational ground state. This represents the first observation of a charge-dipole induced shift in an ultracold setting and opens up many new research directions. The blockade we have observed provides a mechanism for nondestructive state readout of the molecule [36,37]. A single Rydberg atom can also mediate effective spin-spin interactions between a pair of molecular dipoles [87]. For molecules prepared in the N¼2rotational state, our calculations for the Rb(52s) Rydberg state predict that resolvable, deeply bound states exist for separations of ∼220 nm. This offers the possibility to photoassociate giant polyatomic Rydberg molecules [46–48,88]. By selecting Rydberg and molecular states which interact via resonant dipole-dipole interactions, the Rydberg blockade radius can be increased to several microns, enabling high-fidelity entangling gates between molecules mediated by strong interactions with neighboring Rydberg atoms [38,39]. This presents the tantalizing prospect of a hybrid platform where quantum information is transferred between individually trapped molecules using Rydberg atoms. The data presented in this Letter are available from [89]. We thank S. Spence for earlier experimental work, A. L. Tao for assistance in the setup of the STIRAP laser system, X. Yang for informative simulations of the atom and molecule system, and H. J. Williams and S. A. Gardiner for helpful discussions. We acknowledge support from the UK Engineering and Physical Sciences Research Council (EPSRC) Grants EP/P01058X/1, EP/V047302/1, and EP/W00299X/1, UK Research and Innovation (UKRI) Frontier Research Grant EP/X023354/1, the Royal Society, and Durham University. R. G. F. gratefully acknowledges financial support by the Spanish projects PID2020–113390 GB-I00 (MICIN), PY20-00082 (Junta de Andalucía) and A-FQM-52-UGR20 (ERDF-University of Granada), and the Andalusian Research Group FQM207. H. R. 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