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Collisional Cooling and Magnetic Control of Reactions in Ultracold Spin-polarized NaLi+Na Mixture

Hyungmok Son

Published Jan 1, 2022• 0 citations
OpenAlex

Abstract

This thesis describes two studies with a mixture of ultracold triplet ground state 23Na6Li molecules and 23Na atoms. The first study is to realize the cooling of ultracold NaLi molecules with Na atoms that efficiently exchange kinetic energy when colliding with molecules and bring them to thermal equilibrium with lower temperatures. Such cooling based on inter-particle collisions, which is the so-called collisional cooling, has not been successful in other molecular systems at micro-Kelvin temperatures or below before the work described in this thesis. By harnessing the good-to-bad collision ratio of the NaLi+Na mixture around 200, we increase the phase space density of the molecules by a factor of 20, achieving the temperatures as low as 220 nano-Kelvin. This collisional property arises from the suppression of reactive and inelastic collisions by the polarization of the spin in a chemically non-reactive quartet state, possibly together with the small size and the low mass of the NaLi+Na mixture. The loss rate in the spin-polarized NaLi+Na mixture is more than an order of magnitude lower than the so-called universal rate, which occurs in most molecular collisions as particles are lost or react at short range with unity probability. The second study is about the control of the reactive collisions by magnetically-tunable scattering resonances, so-called Feshbach resonances, between molecules and atoms. By controlling the phase of the scattering wavefunction via a Feshbach resonance at 978 G, we modify the loss rate by more than two orders of magnitude, and such a large dynamic range of tunability in loss is possible only in a molecular system in which the background loss is far below the universal limit, like the spin-polarized NaLi+Na mixture. We explain the observed tunability in loss by a single-channel model based on quantum interference of the scattering wavefunction reflected at long and short ranges, which is analogous to the optical interference in a Fabry-Perot resonator. By fitting our Fabry-Perot model to the precisely measured lineshape of the loss feature at 978 G, we measure short range parameters, such as a background phase shift parameter and a quantum-defect parameter, which indicates that the spin-polarized NaLi+Na has about 4% loss probability at short range. By extending the single-channel model to consider the lifetime of a bound state of a closed channel, we treat a weak Feshbach resonance at 1030 G as a lossy phase shifter. With this extended two-channel model, we measure that the lifetime of a three-body collision complex associated with the resonance at 1030 G is about 60 ns. The work of this thesis shows that the spin-polarization is a simple yet powerful method to suppress reactive collisions in a molecular system and establishes the light triplet molecule as a useful system to study quantum chemistry, molecular scattering resonances, and possibly short range physics.

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Li molecules. In most molecular collisions, particles react or are lost near short range with unity probability, leading to the so-called universal rate. By contrast, the Na + NaLi system was shown to have only ~4% loss probability in a fully spin-polarized state. By controlling the phase of the scattering wave function via a Feshbach resonance, we modified the loss rate by more than a factor of 100, from far below to far above the universal limit. The results are explained in analogy with an optical Fabry-Perot resonator by interference of reflections at short and long range. Our work demonstrates quantum control of chemistry by magnetic fields with the full dynamic range predicted by our models.

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Ultracold chemistry operates in a regime where thermal motion is suppressed to the microkelvin scale, allowing quantum mechanics to dictate every aspect of molecular interaction. This paper reviews the theoretical foundations and experimental breakthroughs that now make coherent control of ultracold reactions possible. It first outlines the separation of short- and long-range physics through quantum defect theory, emphasizing why short-range dynamics remain intractable and why universal loss emerges naturally. It then examines how long-range potentials, resonances, and quantum interference enable tunable scattering behavior. Two major milestones anchor this discussion: phase-coherent atom–atom–molecule coupling, which confirms the transfer and control of reaction phase, and the experimental resolution of long-range atom–molecule Feshbach resonances using a Fabry–P´erot interferometer model. Finally, it highlights the recent observation of a magnetically tunable molecule–molecule Feshbach resonance in NaLi, overturning long-held assumptions about the impossibility of resonance control in complex molecular systems. Together, these results demonstrate that ultracold molecules can be engineered to undergo fully coherent, interference-driven reactions, establishing a framework for quantum-controlled chemistry and laying the groundwork for applications in quantum simulation and computation.

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Collisional resonances of molecules can offer a deeper understanding of interaction potentials and collision complexes, and allow control of chemical reactions.Here, we experimentally map out the spectrum of Feshbach resonances in collisions between ultracold triplet rovibrational ground-state NaLi molecules and Na atoms over a range of 1400 G. Preparation of the spin-stretched state puts the system initially into the nonreactive quartet potential.A total of 25 resonances are observed, in qualitative agreement with quantum-chemistry calculations using a coupled-channels approach.Although the theory cannot predict the positions of resonances, it can account for several experimental findings and provide unprecedented insight into the nature and couplings of ultracold, strongly interacting complexes.Previous work has addressed only weakly bound complexes.We show that the main coupling mechanism results from spin-rotation and spin-spin couplings in combination with the anisotropic atom-molecule interaction, and that the collisional complexes which support the resonances have a size of 30a 0 -40a 0 .This study illustrates the potential of a combined experimental and theoretical approach.

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We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a^{3}Σ^{+}) producing singlet Na_{2}(^{1}Σ_{g}^{+}) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a^{3}Σ^{+},v=0,N=0) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial nonreactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the N=2 rotational state of NaLi(a^{3}Σ^{+},v=0) and would thus exist in systems without hyperfine interactions.

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The work described in this thesis can be divided into two parts. The first part is concerned with the production of degenerate Fermi gases and Bose-Fermi mixtures. The second part of the thesis describes studies of strongly interacting spin-mixtures of ultracold fermions. We have cooled a magnetically trapped spin-polarized 6Li Fermi gas into quantum degeneracy by sympathetic cooling with bosonic 23Na. In order to do this, we have converted our previously developed apparatus for Bose-Einstein condensation of 23Na into a two-species cooling facility. We have produced 6Li samples with up to 7 × 107 atoms at temperatures below 0.5TF , and up to 3× 107 atoms at temperatures as low as 0.05TF . Further, we have also produced stable quantum degenerate mixtures of 23Na and 6Li, with several million atoms of each species. In a second set of experiments, we have studied strongly interacting spin-mixtures of 6Li. The strength of interactions was resonantly controlled by applying a magnetic field and tuning to “Feshbach resonances”, which occur when the total energy of the colliding particles coincides with the energy of a bound molecular state. These studies are relevant for the continuing quest for a superfluid transition in a Fermi gas. By studying the inelastic decay of the cloud, we have experimentally identified two Feshbach resonances for the inter-state interactions of the two lowest ground states of 6Li. Most importantly, we found that the lifetime of the strongly interacting system is long enough to observe a superfluid transition in the future. The effects of the coherent collisions in 6Li spin-mixtures were studied using radiofrequency (RF) spectroscopy. We demonstrated the absence of mean field “clock shifts” in a two-state mixture of fermions, and have introduced a three-level method to observe the interaction energy shifts. In the strongly interacting regime, near a Feshbach resonance, we have observed universal behavior of the interaction energy, independent of the value of the scattering length. Finally, we have theoretically studied the effects of Pauli blocking during a free expansion of a degenerate Fermi gas. We have concluded that a strongly interacting normal gas will undergo a hydrodynamic expansion even at zero temperature, due to inefficiency of the Pauli suppression of collisions. Therefore, the already observed hydrodynamic expansion cannot be conclusively interpreted as a signature of superfluidity. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics

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This thesis has investigated the dynamics of ultracold atomic collisions in the presence of both static magnetic and oscillating radio-frequency (rf) fields. The bound state structure and scattering length of 39K+133Cs was examined in the presence of only a static magnetic field, where it was found that no Feshbach resonance of suitable width for magnetoassociation existed at a magnetic field where caesium can be cooled to degeneracy. We then showed that zero-energy Feshbach resonances may be engineered using an rf field in places where they did not previously exist. An rf field with frequency 79.9 MHz was chosen to induce a resonance near 21 G. The widths of such rf-induced Feshbach resonances increase quadratically with rf field strength. The resonances presented are lossless with circularly polarized rf, and the molecules created are long-lived even with plane-polarized RF. Collisional losses in rf-dressed magnetic traps were also investigated. An rf-induced loss mechanism that does not exist in the absence of rf radiation was identified. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings and the strength of the rf field. The results were interpreted in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. 87Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate. For heteronuclear mixtures an rf-modified spin-exchange mechanism was identified that results in loss rates orders of magnitude greater than the rf-induced loss rates in homonuclear cases. Fast loss is expected in mixtures where the Lande g-factors differ.

•Jan 1, 2019•0 citations
This thesis describes two studies with a mixture of ultracold triplet ground state 23Na6Li molecules and 23Na atoms. The first study is to realize the cooling of ultracold NaLi molecules with Na atoms that efficiently exchange kinetic energy when colliding with molecules and bring them to thermal equilibrium with lower temperatures. Such cooling based on inter-particle collisions, which is the so-called collisional cooling, has not been successful in other molecular systems at micro-Kelvin temperatures or below before the work described in this thesis. By harnessing the good-to-bad collision ratio of the NaLi+Na mixture around 200, we increase the phase space density of the molecules by a factor of 20, achieving the temperatures as low as 220 nano-Kelvin. This collisional property arises from the suppression of reactive and inelastic collisions by the polarization of the spin in a chemically non-reactive quartet state, possibly together with the small size and the low mass of the NaLi+Na mixture. The loss rate in the spin-polarized NaLi+Na mixture is more than an order of magnitude lower than the so-called universal rate, which occurs in most molecular collisions as particles are lost or react at short range with unity probability. The second study is about the control of the reactive collisions by magnetically-tunable scattering resonances, so-called Feshbach resonances, between molecules and atoms. By controlling the phase of the scattering wavefunction via a Feshbach resonance at 978 G, we modify the loss rate by more than two orders of magnitude, and such a large dynamic range of tunability in loss is possible only in a molecular system in which the background loss is far below the universal limit, like the spin-polarized NaLi+Na mixture. We explain the observed tunability in loss by a single-channel model based on quantum interference of the scattering wavefunction reflected at long and short ranges, which is analogous to the optical interference in a Fabry-Perot resonator. By fitting our Fabry-Perot model to the precisely measured lineshape of the loss feature at 978 G, we measure short range parameters, such as a background phase shift parameter and a quantum-defect parameter, which indicates that the spin-polarized NaLi+Na has about 4% loss probability at short range. By extending the single-channel model to consider the lifetime of a bound state of a closed channel, we treat a weak Feshbach resonance at 1030 G as a lossy phase shifter. With this extended two-channel model, we measure that the lifetime of a three-body collision complex associated with the resonance at 1030 G is about 60 ns. The work of this thesis shows that the spin-polarization is a simple yet powerful method to suppress reactive collisions in a molecular system and establishes the light triplet molecule as a useful system to study quantum chemistry, molecular scattering resonances, and possibly short range physics.
Li molecules. In most molecular collisions, particles react or are lost near short range with unity probability, leading to the so-called universal rate. By contrast, the Na + NaLi system was shown to have only ~4% loss probability in a fully spin-polarized state. By controlling the phase of the scattering wave function via a Feshbach resonance, we modified the loss rate by more than a factor of 100, from far below to far above the universal limit. The results are explained in analogy with an optical Fabry-Perot resonator by interference of reflections at short and long range. Our work demonstrates quantum control of chemistry by magnetic fields with the full dynamic range predicted by our models.
Ultracold chemistry operates in a regime where thermal motion is suppressed to the microkelvin scale, allowing quantum mechanics to dictate every aspect of molecular interaction. This paper reviews the theoretical foundations and experimental breakthroughs that now make coherent control of ultracold reactions possible. It first outlines the separation of short- and long-range physics through quantum defect theory, emphasizing why short-range dynamics remain intractable and why universal loss emerges naturally. It then examines how long-range potentials, resonances, and quantum interference enable tunable scattering behavior. Two major milestones anchor this discussion: phase-coherent atom–atom–molecule coupling, which confirms the transfer and control of reaction phase, and the experimental resolution of long-range atom–molecule Feshbach resonances using a Fabry–P´erot interferometer model. Finally, it highlights the recent observation of a magnetically tunable molecule–molecule Feshbach resonance in NaLi, overturning long-held assumptions about the impossibility of resonance control in complex molecular systems. Together, these results demonstrate that ultracold molecules can be engineered to undergo fully coherent, interference-driven reactions, establishing a framework for quantum-controlled chemistry and laying the groundwork for applications in quantum simulation and computation.
Collisional resonances of molecules can offer a deeper understanding of interaction potentials and collision complexes, and allow control of chemical reactions.Here, we experimentally map out the spectrum of Feshbach resonances in collisions between ultracold triplet rovibrational ground-state NaLi molecules and Na atoms over a range of 1400 G. Preparation of the spin-stretched state puts the system initially into the nonreactive quartet potential.A total of 25 resonances are observed, in qualitative agreement with quantum-chemistry calculations using a coupled-channels approach.Although the theory cannot predict the positions of resonances, it can account for several experimental findings and provide unprecedented insight into the nature and couplings of ultracold, strongly interacting complexes.Previous work has addressed only weakly bound complexes.We show that the main coupling mechanism results from spin-rotation and spin-spin couplings in combination with the anisotropic atom-molecule interaction, and that the collisional complexes which support the resonances have a size of 30a 0 -40a 0 .This study illustrates the potential of a combined experimental and theoretical approach.
We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a^{3}Σ^{+}) producing singlet Na_{2}(^{1}Σ_{g}^{+}) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a^{3}Σ^{+},v=0,N=0) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial nonreactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the N=2 rotational state of NaLi(a^{3}Σ^{+},v=0) and would thus exist in systems without hyperfine interactions.
The work described in this thesis can be divided into two parts. The first part is concerned with the production of degenerate Fermi gases and Bose-Fermi mixtures. The second part of the thesis describes studies of strongly interacting spin-mixtures of ultracold fermions. We have cooled a magnetically trapped spin-polarized 6Li Fermi gas into quantum degeneracy by sympathetic cooling with bosonic 23Na. In order to do this, we have converted our previously developed apparatus for Bose-Einstein condensation of 23Na into a two-species cooling facility. We have produced 6Li samples with up to 7 × 107 atoms at temperatures below 0.5TF , and up to 3× 107 atoms at temperatures as low as 0.05TF . Further, we have also produced stable quantum degenerate mixtures of 23Na and 6Li, with several million atoms of each species. In a second set of experiments, we have studied strongly interacting spin-mixtures of 6Li. The strength of interactions was resonantly controlled by applying a magnetic field and tuning to “Feshbach resonances”, which occur when the total energy of the colliding particles coincides with the energy of a bound molecular state. These studies are relevant for the continuing quest for a superfluid transition in a Fermi gas. By studying the inelastic decay of the cloud, we have experimentally identified two Feshbach resonances for the inter-state interactions of the two lowest ground states of 6Li. Most importantly, we found that the lifetime of the strongly interacting system is long enough to observe a superfluid transition in the future. The effects of the coherent collisions in 6Li spin-mixtures were studied using radiofrequency (RF) spectroscopy. We demonstrated the absence of mean field “clock shifts” in a two-state mixture of fermions, and have introduced a three-level method to observe the interaction energy shifts. In the strongly interacting regime, near a Feshbach resonance, we have observed universal behavior of the interaction energy, independent of the value of the scattering length. Finally, we have theoretically studied the effects of Pauli blocking during a free expansion of a degenerate Fermi gas. We have concluded that a strongly interacting normal gas will undergo a hydrodynamic expansion even at zero temperature, due to inefficiency of the Pauli suppression of collisions. Therefore, the already observed hydrodynamic expansion cannot be conclusively interpreted as a signature of superfluidity. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacArthur Professor of Physics
This thesis has investigated the dynamics of ultracold atomic collisions in the presence of both static magnetic and oscillating radio-frequency (rf) fields. The bound state structure and scattering length of 39K+133Cs was examined in the presence of only a static magnetic field, where it was found that no Feshbach resonance of suitable width for magnetoassociation existed at a magnetic field where caesium can be cooled to degeneracy. We then showed that zero-energy Feshbach resonances may be engineered using an rf field in places where they did not previously exist. An rf field with frequency 79.9 MHz was chosen to induce a resonance near 21 G. The widths of such rf-induced Feshbach resonances increase quadratically with rf field strength. The resonances presented are lossless with circularly polarized rf, and the molecules created are long-lived even with plane-polarized RF. Collisional losses in rf-dressed magnetic traps were also investigated. An rf-induced loss mechanism that does not exist in the absence of rf radiation was identified. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings and the strength of the rf field. The results were interpreted in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. 87Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate. For heteronuclear mixtures an rf-modified spin-exchange mechanism was identified that results in loss rates orders of magnitude greater than the rf-induced loss rates in homonuclear cases. Fast loss is expected in mixtures where the Lande g-factors differ.