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Coherence and Collisions in Ultracold $^{87}$Rb$^{133}$Cs Molecules

Jacob A. Blackmore

Published Jan 1, 2020• 0 citations
OpenAlex

Abstract

This thesis presents work towards the development of a quantum simulator based on $^{87}$Rb$^{133}$Cs molecules using a bulk sample of up to ~4000 molecules at temperatures of ~1 µK. We demonstrate coherent control over the molecules' internal state using resonant microwave fields. We test this coherence by performing high resolution Ramsey spectroscopy of the first rotational transition and observing how the contrast of the spectroscopic fringes decay. We are able to affect the coherence of the superposition using an external laser field, as the two component states have a significant differential AC Stark shift. We extend this microwave control by including an additional microwave field, demonstrating the Autler-Townes effect with hyperfine state resolution and transfer between two hyperfine states in $N=0$. We study the internal structure of the molecule in the presence of external fields focussing on controlling the differential AC Stark shift between the rotational ground state and the first excited state. We investigate the effect of the off-resonant light on the internal structure in static magnetic and electric fields. In the DC electric field we use two models to describe the molecular structure, demonstrating that at modest values of the electric field the nuclear spin angular momentum is decoupled from the rotational angular momentum of the molecule, this enables us to construct a set of optimum trapping parameters for states with $M_N=0$. Through careful measurements of the molecular lifetime we are able to determine that molecular losses are limited by two-body collisions. By introducing a time dependent intensity modulation to our optical trap we are further able to determine that the dominant loss process in bulk samples of ultracold $^{87}$Rb$^{133}$Cs molecules is the laser excitation of collision complexes. Finally, we investigate the collisional properties of $^{87}$Rb$^{133}$Cs with $^{87}$Rb and $^{133}$Cs atoms. We find that the loss is caused by single molecule-single atom collisions and sub-universal over a wide range of magnetic fields.

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Coherence and Collisions in Ultracold 87^{87}87Rb133^{133}133Cs Molecules
This thesis presents work towards the development of a quantum simulator based on 87^{87}87Rb133^{133}133Cs molecules using a bulk sample of up to ~4000 molecules at temperatures of ~1 µK. We demonstrate coherent control over the molecules' internal state using resonant microwave fields. We test this coherence by performing high resolution Ramsey spectroscopy of the first rotational transition and observing how the contrast of the spectroscopic fringes decay. We are able to affect the coherence of the superposition using an external laser field, as the two component states have a significant differential AC Stark shift. We extend this microwave control by including an additional microwave field, demonstrating the Autler-Townes effect with hyperfine state resolution and transfer between two hyperfine states in N=0N=0N=0. We study the internal structure of the molecule in the presence of external fields focussing on controlling the differential AC Stark shift between the rotational ground state and the first excited state. We investigate the effect of the off-resonant light on the internal structure in static magnetic and electric fields. In the DC electric field we use two models to describe the molecular structure, demonstrating that at modest values of the electric field the nuclear spin angular momentum is decoupled from the rotational angular momentum of the molecule, this enables us to construct a set of optimum trapping parameters for states with MN=0M_N=0MN​=0. Through careful measurements of the molecular lifetime we are able to determine that molecular losses are limited by two-body collisions. By introducing a time dependent intensity modulation to our optical trap we are further able to determine that the dominant loss process in bulk samples of ultracold 87^{87}87Rb133^{133}133Cs molecules is the laser excitation of collision complexes. Finally, we investigate the collisional properties of 87^{87}87Rb133^{133}133Cs with 87^{87}87Rb and 133^{133}133Cs atoms. We find that the loss is caused by single molecule-single atom collisions and sub-universal over a wide range of magnetic fields.
Polar molecules offer a new platform for quantum simulation of systems with long-range interactions, based on the electrostatic interaction between their electric dipole moments. Here, we report the development of coherent quantum state control using microwave fields in 40 Ca 19 F and 87 Rb 133 Cs molecules, a crucial ingredient for many quantum simulation applications. We perform Ramsey interferometry measurements with fringe spacings of ∼1 kHz and investigate the dephasing time of a superposition of N = 0 and N = 1 rotational states when the molecules are confined. For both molecules, we show that a judicious choice of molecular hyperfine states minimises the impact of spatially varying transition-frequency shifts across the trap. For magnetically trapped 40 Ca 19 F we use a magnetically insensitive transition and observe a coherence time of 0.61(3) ms. For optically trapped 87 Rb 133 Cs we exploit an avoided crossing in the AC Stark shifts and observe a maximum coherence time of 0.75(6) ms.
This thesis presents the development of a toolbox for the coherent control of ultracold polar molecules. Such systems of molecules promise the creation of long-lived, highly dipolar quantum gases with applications spanning the fields of quantum state controlled chemistry, quantum information, quantum simulation, and precision measurement. However, the addition of vibrational and rotational degrees of freedom leads to molecular systems being significantly more complex than their widely used atomic counterparts. In this work we demonstrate full control of the quantum state down to the hyperfine level of an optically trapped sample of ultracold bosonic 87Rb133 Cs molecules, and exploit that control to begin an investigation into the collision processes which take place in an ultracold molecular gas. We create a sample of up to ∼ 4000 optically trapped molecules in their rovibronic and hyperfine ground state. We characterise the molecules by measuring their temperature, binding energy, and molecule-frame electric dipole moment. We perform spectroscopy of the first rotationally excited state with hyperfine state resolution using microwaves to determine accurate values of rotational and hyperfine coupling constants. We use coherent π pulses to perform complete transfer population between selected hyperfine levels of the ground, first-excited, and second-excited rotational states. We investigate the effect of the off-resonant light of our optical dipole trap on the rotational and hyperfine structure of the molecules. Through a combination of high-resolution microwave spectroscopy and parametric heating measurements, we characterise the polarisability of the 87Rb133Cs molecule. We demonstrate that coupling between neighbouring hyperfine states manifests in rich structure with many avoided crossings in any rotational state other than the ground state. This coupling may be tuned by rotating the polarisation of the linearly polarised trapping light. Finally, we study the lifetime of polar bosonic 87Rb133Cs molecules in our 3D optical dipole trap. We examine the lifetime of the molecules as a function of dipole trap intensity, magnetic field, and hyperfine and rotational state. Despite the chemical stability of the 87Rb133 Cs molecule, we observe lifetimes of ∼1 s corresponding to 2-body decay rates close to the universal limit.
Ultracold polar molecules possess a manifold of long-lived molecular rotational states, which can be coherently controlled using microwave fields and entangled by the long-range dipole-dipole interactions between molecules. The ability to control these features at the individual molecule level provides a rich toolbox with which to engineer quantum simulations of exotic materials or build a molecular quantum computer. Until recently, this level of single molecule control has eluded researchers due to the challenges inherent in taming the complex internal structure of molecules. In this thesis, we demonstrate full control over the internal quantum states and coherent interactions of individual NaCs molecules in optical tweezers. This platform is based on coherent assembly of ultracold Na and Cs atoms trapped and cooled in separate arrays, before being magnetoassociated at a Feshbach resonance to form weakly-bound molecules. Using high-resolution spectroscopy of electronically excited molecular states, we identify an efficient two-photon pathway to the rovibrational ground state of NaCs that we use to prepare an array of ground state molecules in tweezers. We demonstrate a "magic ellipticity'' technique to eliminate differential light shifts between two molecular rotational states and achieve coherence times of up to 250(40) ms for a superposition of those states. We then show that we can rearrange molecules in an array to eliminate defects and perform single-shot readout of multiple rotational states using controlled molecule dissociation and imaging of constituent atoms at high magnetic field. Finally, we coherently control the dipole-dipole interactions between two molecules, producing a Bell state with a fidelity of 94(3) % and demonstrating a universal entangling iSWAP gate for qubits encoded in molecular hyperfine states.
We explore coherent multi-photon processes in 87Rb133Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of 87Rb133Cs up to N = 6, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient Dv = h × 207.3(2) Hz.
The thesis reports transferring the ultracold RbCs molecules to the absolute ground state and a trapping light that eliminates the differential AC Stark shift. We build a laser system to perform Stimulated Raman Adiabatic Passage (STIRAP) for the molecules trapped in tweezers, which transfer the molecules from the weakly- bounded state to the absolute ground state. We use the offset cavity stabilisation technique to stabilise the laser frequencies to a passive cavity to narrow the laser linewidths while keeping the laser frequency tunable. We then align the beams to the molecules. We demonstrate a “magic” laser frequency to eliminate the differential AC Stark shift of the rotational states in the ground vibrational state of RbCs molecule and to increase the rotational coherence time of multiple states. We study the AC Stark effect caused by the trapping light. We calculate the polarisabilities of the rotational states near a narrow electronic from X ^1Σ^+ state to b^3Π_0 state and found at certain laser frequency the polarisabilities become the same. We measure the transition frequencies to different vibrational states in the excited electronic state experimentally. We perform microwave spectroscopy to measure the light shift and show that the shift vanishes at the magic frequency. We confirmed the coherence in 1 ms timescale by measuring the Ramsey fringe contrast.
Abstract Understanding ultracold collisions involving molecules is of fundamental importance for current experiments, where inelastic collisions typically limit the lifetime of molecular ensembles in optical traps. Here we present a broad study of optically trapped ultracold RbCs molecules in collisions with one another, in reactive collisions with Rb atoms, and in nonreactive collisions with Cs atoms. For experiments with RbCs alone, we show that by modulating the intensity of the optical trap, such that the molecules spend 75% of each modulation cycle in the dark, we partially suppress collisional loss of the molecules. This is evidence for optical excitation of molecule pairs mediated via sticky collisions. We find that the suppression is less effective for molecules not prepared in the spin-stretched hyperfine ground state. This may be due either to longer lifetimes for complexes in the dark or to laser-free decay pathways. For atom–molecule mixtures, RbCs + Rb and RbCs + Cs, we demonstrate that the rate of collisional loss of molecules scales linearly with the density of atoms. This indicates that, in both cases, the loss of molecules is rate-limited by two-body atom–molecule processes. For both mixtures, we measure loss rates that are below the thermally averaged universal limit.