We report the first detailed decay studies of trapped metastable (2S) hydrogen. By two-photon excitation of ultracold H samples, we have produced clouds of at least 5x10^7 magnetically trapped 2S atoms at densities greater than 4x10^10 cm^-3 and temperatures below 100 \muK. We derive experimental values for the total 2S-2S two-body loss rate constant in this temperature regime. Our results are in the range of recent theoretical calculations. We also find experimental upper limits on the rate constant for loss due to inelastic 1S-2S collisions.
We report measurement of inelastic loss in dense and cold metastable ytterbium (Yb[$^3P_2$]). Use of an optical far-off-resonance trap enables us to trap atoms in all magnetic sublevels, removing multichannel collisional trap loss from the system. Trapped samples of Yb[$^3P_2$] are produced at a density of 2$\times10^{13}$ cm$^{-3}$ and temperature of 2 $μ$K. We observe rapid two-body trap loss of Yb[$^3P_2$] and measure the inelastic collision rate constant 1.0(3)$\times10^{-11}$ cm$^3$s$^{-1}$. The existence of the fine-structure changing collisions between atoms in the $^3P_2$ state is stro…
We report on the realization of an ultracold (<25~muK) mixture of rubidium ({87}Rb) and metastable triplet helium ({4}He) in an optical dipole trap. Our scheme involves laser cooling in a dual-species magneto-optical trap, simultaneous MW- and RF-induced forced evaporative cooling in a quadrupole magnetic trap, and transfer to a single-beam optical dipole trap. We observe long trapping lifetimes for the doubly spin-stretched spin-state mixture and measure much shorter lifetimes for other spin-state combinations. We discuss prospects for realizing quantum degenerate mixtures of alkali-metal and…
We study binary collisions of metastable calcium atoms ($^{40}$Ca) in an optical dipole trap. Collisions between $^{3}$P$_{0}$-atoms and between $^{3}$P$_{0}$ and $^{1}$S$_{0}$-atoms are considered. In the former case, the elastic and inelastic collision parameters are found to be $5.4\times 10^{-11}\,\mathrm{cm}^{3}\mathrm{s}^{-1}$ and $3.6\times 10^{-11}\,\mathrm{cm}^{3}\mathrm{s}^{-1}$, respectively. A fraction of the collisions between $^{3}$P$_{0}$-atoms is found to produce cold trapped atoms in the singlet $^{1}$S$_{0}$ state, suggesting that the internal energy for these collisions is d…
We present a multichannel scattering calculation of elastic and inelastic cold collisions between two low-field seeking, metastable ^{88}Sr [(5s5p) ^3P_2] atoms in the presence of an external magnetic field. The scattering physics is governed by strong anisotropic long-range interactions, which lead to pronounced coupling among the partial waves of relative motion. As a result, nonadiabatic transitions are shown to trigger a high rate of inelastic losses. At relatively high energies, T > 100 mkK, the total inelastic collision rate is comparable with the elastic rate. However, at lower collisio…
We have observed thermalization by elastic collisions of magnetically trapped metastable helium atoms. Our method directly samples the reconstruction of a thermal energy distribution after the application of an RF knife. The relaxation time of our sample towards equilibrium gives an elastic collision rate constant close to the unitarity limit.
We review experimental and theoretical work on cold, trapped metastable noble gases. We em- phasize the aspects which distinguish work with these atoms from the large body of work on cold, trapped atoms in general. These aspects include detection techniques and collision processes unique to metastable atoms. We describe several experiments exploiting these unique features in fields including atom optics and statistical physics. We also discuss precision measurements on these atoms including fine structure splittings, isotope shifts, and atomic lifetimes.
Quantum computers, much like their classical counterparts, will likely benefit from flexible qubit encodings that can be matched to different tasks. For trapped ion quantum processors, a common way to access multiple encodings is to use multiple, co-trapped atomic species. Here, we outline an alternative approach that allows flexible encoding capabilities in single-species systems through the use of long-lived metastable states as an effective, programmable second species. We describe the set of additional trapped ion primitives needed to enable this protocol and show that they are compatible …
Spin-polarized metastable atoms of ultracold ytterbium are trapped at high density and their inelastic collisional properties are measured. We reveal that in collisions of Yb(3P2) with Yb(1S0) there is relatively weak inelastic loss, but with a significant spin-dependence consistent with Zeeman sublevel changes as being the dominant decay process. This is in strong contrast to our observations of Yb(3P2)-Yb(3P2) collisional loss, which are, at low field, much more rapid and have essentially no spin dependence. Our results give a guideline to use the 3P2 states in many possible applications.
We report the measurement of one-body loss rates for magnetically trapped metastable europium atoms and the study of their loss mechanism. The loss of atoms observed in a magneto-optical trap is not fully understood because of the indivisibility of the loss regarding optical pumpings due to the presence of cooling laser beams. We magnetically trapped the atoms by directly loading from the magneto-optical trap and observed almost identical one-body loss rates of approximately $2.6\,\mathrm{s^{-1}}$ for two isotopes: $\mathrm{{}^{151}Eu}$ and $\mathrm{{}^{153}Eu}$. Our rate-equation-based model,…
We present an experimental scheme which combines the well established method of velocity-mapimaging, with a cold trapped metastable neon target. The device is used for obtaining the branching ratios and recoil-ion energy distributions for the penning ionization process in optical collisions of ultracold metastable neon. The potential depth of the highly excited dimer potential is extracted and compared with theoretical calculations. The simplicity to construct, characterize and apply such a device, makes it a unique tool for the low-energy nuclear physics community, enabling opportunities for …
Experimentally the spin dependence of inelastic collisions between ytterbium (Yb) in the metastable 3P0 state and lithium (Li) in the Li ground state manifold is investigated at low magnetic fields. Using selective excitation all magnetic sublevels mJ of 174Yb(3P0) are accessed and four of the six lowest lying magnetic sublevels of 6Li are prepared by optical pumping. On the one hand, mJ-independence of collisions involving Li(F=1/2) atoms is found. A systematic mJ-dependence in collisions with Li(F=3/2) atoms, in particular suppressed losses for stretched collisional states, is observed on th…
A single bichromatic field near-resonant to a qubit transition is typically used for $\hatσ_x$ or $\hatσ_y$ Mølmer-Sørensen type interactions in trapped ion systems. Using this field configuration, it is also possible to synthesize a $\hatσ_z$ spin-dependent force by merely adjusting the beat-note frequency. Here, we expand on previous work and present a comprehensive theoretical and experimental investigation of this scheme with a laser near-resonant to a quadrupole transition in $^{88}$Sr$^+$. Further, we characterise its robustness to optical phase and qubit frequency offsets, and demonstra…
Engineering magnetically insensitive qubits in metastable electronic D-states of trapped ions
IonQ, Inc.（IonQ公司）；Joint Quantum Institute and Department of Physics, University of Maryland（马里兰大学联合量子研究所与物理系）；Infleqtion, Inc.（Infleqtion公司）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Keysight Technologies（是德科技）；Duke Quantum Center, Department of Electrical and Computer Engineering and Department of Physics, Duke University（杜克大学电气与计算机工程系、物理系及杜克量子中心）
We report scattering lengths for the singlet Sigma g +, triplet Sigma u + and quintet Sigma g + adiabatic molecular potentials relevant to collisions of two metastable (n=2 triplet S) helium atoms as a function of the uncertainty in these potentials. These scattering lengths are used to calculate experimentally observable scattering lengths, elastic cross sections and inelastic rates for any combination of states of the colliding atoms, at temperatures where the Wigner threshold approximation is valid.
Magneto-optically trapped atoms enable the determination of lifetimes of metastable states and higher lying excited states like the $\rm{5d^{2}~^{3}F_{2}}$ state in barium. The state is efficiently populated by driving strong transitions from metastable states within the cooling cycle of the barium MOT. The lifetime is inferred from the increase of MOT fluorescence after the transfer of up to $30\,\%$ of the trapped atoms to this state. The radiative decay of the $\rm{5d^{2}~^{3}F_{2}}$ state cascades to the cooling cycle of the MOT with a probability of $96.0(7)\,\%$ corresponding to a trap l…
We report the fast accumulation of a large number of metastable 52Cr atoms in a mixed trap, formed by the superposition of a strongly confining optical trap and a quadrupolar magnetic trap. The steady state is reached after about 400 ms, providing a cloud of more than one million metastable atoms at a temperature of about 100 microK, with a peak density of 10^{18} atoms.m^{-3}. We have optimized the loading procedure, and measured the light shift of the 5D4 state by analyzing how the trapped atoms respond to a parametric excitation. We compare this result to a theoretical evaluation based on t…
Radiative decay from the excited $^1P_1$ state to metastable $^3P_2$ and $^3P_0$ states is expected to limit attainable trapped atomic population in a magneto-optic trap of ytterbium (Yb) atoms. In experiments we have carried out with optical repumping of $^3P_{0,2}$ states to $^3P_1$, we observe enhancement of trapped atoms yield in the excited $^1P_1$ state. The individual decay rate to each metastable state is measured and the results show an excellent agreement with the theoretical values.
Metastable calcium atoms, produced in a magneto-optic trap (MOT) operating within the singlet system, are continuously loaded into a magnetic trap formed by the magnetic quadrupole field of the MOT. At MOT temperatures of 3 mK and 240 ms loading time we observe 1.1 x 10^8 magnetically trapped 3P2 atoms at densities of 2.4 x 10^8 cm^-3 and temperatures of 0.61 mK. In a modified scheme we first load a MOT for metastable atoms at a temperature of 0.18 mK and subsequently release these atoms into the magnetic trap. In this case 240 ms of loading yields 2.4 x 10^8 trapped 3P2 atoms at a peak densit…
We have investigated cold ionizing heteronuclear collisions in dilute mixtures of metastable (2 3S1) 3He and 4He atoms, extending our previous work on the analogous homonuclear collisions [R. J. W. Stas et al., PRA 73, 032713 (2006)]. A simple theoretical model of such collisions enables us to calculate the heteronuclear ionization rate coefficient, for our quasi-unpolarized gas, in the absence of resonant light (T = 1.2 mK): K34(th) = 2.4*10^-10 cm^3/s. This calculation is supported by a measurement of K34 using magneto-optically trapped mixtures containing about 1*10^8 atoms of each species,…
We report the magnetic trapping of metastable $^3P_2$ atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole allowed $^1S_0-^1P_1$ transition at 461 nm. Decay via $^1P_1\to {^1D_2}\to {^3P_2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over $10^8$ atoms at a density of $8 \times 10^9$ cm$^{-3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energy of atoms as they are transferred from the MOT. This suggests that thermalizat…
Cold inelastic collisions between confined cesium (Cs) atoms and Cs$\_2$ molecules are investigated inside a CO$\_2$ laser dipole trap. Inelastic atom-molecule collisions can be observed and measured with a rate coefficient of $\sim 2.5 \times 10^{-11} $cm$^3$ s$^{-1}$, mainly independent of the molecular ro-vibrational state populated. Lifetimes of purely atomic and molecular samples are essentially limited by rest gas collisions. The pure molecular trap lifetime ranges 0,3-1 s, four times smaller than the atomic one, as is also observed in a pure magnetic trap. We give an estimation of the i…
We report the first direct excitation of the strongly forbidden 5s2 1S0-5s5p 3P0 transition in 87Sr. Its frequency is 429 228 004 235 (20) kHz. A resonant laser creates a small leak in a magneto-optical trap (MOT): atoms build up to the metastable 3P0 state and escape the trapping process, leading to a detectable decrease in the MOT fluorescence. This line has a natural width of 10^{-3} Hz and can be used for a new generation of optical frequency standards using atoms trapped in a light shift free dipole trap.
We trap cold, ground-state, argon atoms in a deep optical dipole trap produced by a build-up cavity. The atoms, which are a general source for the sympathetic cooling of molecules, are loaded in the trap by quenching them from a cloud of laser-cooled metastable argon atoms. Although the ground state atoms cannot be directly probed, we detect them by observing the collisional loss of co-trapped metastable argon atoms using a new type of parametric loss spectroscopy. Using this technique we also determine the polarizability ratio between the ground and the metastable 4s[3/2]$_2$ state to be 40$\…
The loss of ultracold trapped atoms in the vicinity of a Feshbach resonance is treated as a two-stage reaction, using the Breit-Wigner theory. The first stage is the formation of a resonant diatomic molecule, and the second one is its deactivation by inelastic collisions with other atoms. This model is applied to the analysis of recent experiments on $^{87}$Rb, leading to an estimated value of $7\times 10^{-11}$ cm$^{3}/$s for the deactivation rate coefficient.
Experiments on one- and two-photon laser excitation of 232Th+ ions in a radiofrequency ion trap are reported. As the first excitation step, the strongest resonance line at 402 nm from the 6d^2 7s J=3/2 ground state to the 6d7s7p J=5/2 state at 24874 cm^{-1} is driven by radiation from an extended cavity diode laser. Spontaneous decay of the intermediate state populates a number of low-lying metastable states, thus limiting the excited state population and fluorescence signal obtainable with continuous laser excitation. We study the collisional quenching efficiency of helium, argon, and nitroge…
We demonstrate enhanced loading of strontium atoms into a magneto-optical trap using a repumping scheme from the metastable state via the doubly-excited state $5\mathrm{s}5\mathrm{p}\,^3\mathrm{P}_2 \rightarrow 5\mathrm{p}^2\,^3\mathrm{P}_2$ at $481~\mathrm{nm}$. The number of trapped atoms is increased by an order of magnitude. The frequency and intensity dependence of the atom number enhancement, with respect to the non-repumping case, is well reproduced by a simple rate equation model, which also describes single-laser repumping schemes reported previously. The repumping scheme is limited b…
We have constructed a magneto-optical trap (MOT) for metastable triplet helium atoms utilizing the 2 3S1 -> 3 3P2 line at 389 nm as the trapping and cooling transition. The far-red-detuned MOT (detuning Delta = -41 MHz) typically contains few times 10^7 atoms at a relatively high (~10^9 cm^-3) density, which is a consequence of the large momentum transfer per photon at 389 nm and a small two-body loss rate coefficient (2 * 10^-10 cm^3/s < beta < 1.0 * 10^-9 cm^3/s). The two-body loss rate is more than five times smaller than in a MOT on the commonly used 2 3S1 -> 2 3P2 line at 1083 nm. Further…
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique develo…
The Formation of metastable molecules (Feshbach resonances) at the collision of two atoms and subsequent stimulated transition to a lower unbound electronic molecular state, with emission of a photon of the laser radiation has been investigated. This can develop, in particular, for $Rb_2$ molecules due to resonance scattering of two $Rb$ atoms. The considered process is a basis for the creation of excimer lasers. Expressions for the cross sections of elastic and inelastic resonance scattering and the intensity of the stimulated emission of the photons have been obtained.
We consider how trapped molecules can be sympathetically cooled by ultracold atoms. As a prototypical system, we study LiH molecules co-trapped with ultracold Li atoms. We calculate the elastic and inelastic collision cross sections of LiH + Li with the molecules initially in the ground state and in the first rotationally excited state. We then use these cross sections to simulate sympathetic cooling in a static electric trap, an ac electric trap, and a microwave trap. In the static trap we find that inelastic losses are too great for cooling to be feasible for this system. The ac and microwav…
We present an experimental study on the rotational inelastic scattering of OH ($X^2Π_{3/2}, J=3/2, f$) radicals with He and D$_2$ at collision energies between 100 and 500 cm$^{-1}$ in a crossed beam experiment. The OH radicals are state selected and velocity tuned using a Stark decelerator. Relative parity-resolved state-to-state inelastic scattering cross sections are accurately determined. These experiments complement recent low-energy collision studies between trapped OH radicals and beams of He and D$_2$ that are sensitive to the total (elastic and inelastic) cross sections (Sawyer \emph{…
We report on the Stark deceleration and electrostatic trapping of $^{14}$NH ($a ^1Δ$) radicals. In the trap, the molecules are excited on the spin-forbidden $A ^3Π\leftarrow a ^1Δ$ transition and detected via their subsequent fluorescence to the $X ^3Σ^-$ ground state. The 1/e trapping time is 1.4 $\pm$ 0.1 s, from which a lower limit of 2.7 s for the radiative lifetime of the $a ^1Δ, v=0,J=2$ state is deduced. The spectral profile of the molecules in the trapping field is measured to probe their spatial distribution. Electrostatic trapping of metastable NH followed by optical pumping of the t…
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ε/\hbar ω_0}$, where $ε$ is the kinetic en…
The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-field-seeking to strong-field-seeking states are estimated using a simple model. The rates are found to be quite large, of order 10^{-12} - 10^{-10} cm^3/sec, and moreover to grow rapidly in an externally applied electric field. It is argued that these results are generic for polar molecules, and that therefore polar molecules should be trapped by other than electrostatic means.
We have trapped cesium atoms over many minutes in the focus of a CO$_2$-laser beam employing an extremely simple laser system. Collisional properties of the unpolarized atoms in their electronic ground state are investigated. Inelastic binary collisions changing the hyperfine state lead to trap loss which is quantitatively analyzed. Elastic collisions result in evaporative cooling of the trapped gas from 25 $μ$K to 10 $μ$K over a time scale of about 150 s.
We measure inelastic collisional cross sections for the ground $^3$F$_2$ state and the excited $^3$P$_0$ state of atomic thorium in cold collisions with $^3$He. We determine for Th ($^3$F$_2$) at 800 mK the ratio $γ\approx 500$ of the momentum-transfer to Zeeman relaxation cross sections for collisions with $^3$He. For Th ($^3$P$_0$), we study electronic inelastic processes and find no quenching even after $10^6$ collisions. We also determine the radiative lifetime of Th ($^3$P$_0$) to be $τ> 130$ ms. This great stability of the metastable state opens up the possibility for further study, incl…
In an ultracold, optically trapped mixture of $^{87}$Rb and metastable triplet $^4$He atoms we have studied trap loss for different spin-state combinations, for which interspecies Penning ionization is the main two-body loss process. We observe long trapping lifetimes for the purely quartet spin-state combination, indicating strong suppression of Penning ionization loss by at least two orders of magnitude. For the other spin-mixtures we observe short lifetimes that depend linearly on the doublet character of the entrance channel. We compare the extracted loss rate coefficient with recent predi…
Possible evidence for the production of Ar$_2^{*-}$ metastable negative molecular ions in gaseous argon of two-phase detectors for dark matter searches
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ε/\hbar ω_0}$, where $ε$ is the kinetic en…
We establish an experimental method for a detailed investigation of inelastic collisional properties between ytterbium (Yb) in the metastable ${}^3\mathrm{P}_2$ state and ground state lithium (Li). By combining an optical lattice and a direct excitation to the ${}^3\mathrm{P}_2$ state we achieve high selectivity on the collisional partners. Using this method we determine inelastic loss coefficients in collisions between $^{174}$Yb(${}^3\mathrm{P}_2$) with magnetic sublevels of $m_J=0$ and $-2$ and ground state $^6$Li to be $(4.4\pm0.3)\times10^{-11}~\mathrm{cm}^3/\mathrm{s}$ and $(4.7\pm0.8)\t…
We report on the formation of a stable quantum degenerate mixture of fermionic $^6$Li and bosonic $^{133}$Cs in an optical trap by sympathetic cooling near an interspecies Feshbach resonance. New regimes of the quantum degenerate mixtures are identified. With moderate attractive interspecies interactions, we show that a degenerate Fermi gas of Li can be fully confined in the Cs condensate without external potentials. For stronger attraction where mean-field collapse is expected, no such instability is observed. In this case, we suggest the stability is a result of dynamic equilibrium, where th…
We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the ro-vibrational ground state of a $^2Σ$ electronic state and the Zeeman state with the electron spin projection $M_S=1/2$ on the magnetic field axis. This is the lowest-energy state of $^2Σ$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule - molecule interaction potentials, which yields the expectation intervals for the cross sections and the elastic-to-inelastic cross section ratios. We find that the elastic-to-inelastic c…
We observe two-body loss of ${}^3P_0$ ${}^{87}$Sr atoms trapped in a one-dimensional optical lattice. We measure loss rate coefficients for atomic samples between 1 and 6 $μ$K that are prepared either in a single nuclear-spin-sublevel or with equal populations in two sublevels. The measured temperature and nuclear spin preparation dependence of rate coefficients agree well with calculations and reveal that rate coefficients for distinguishable atoms are only slightly enhanced over those of indistinguishable atoms. We further observe a suppression of excitation and losses during interrogation o…
Reaching high densities is a key step towards cold-collision experiments with polyatomic molecules. We use a cryofuge to load up to 2$\times10^7$ CH$_3$F molecules into a box-like electric trap, achieving densities up to 10$^7$/cm$^3$ at temperatures around 350 mK where the elastic dipolar cross-section exceeds 7$\times$10$^{-12}$cm$^2$. We measure inelastic rate constants below 4$\times$10$^{-8}$cm$^3$/s and control these by tuning a homogeneous electric field that covers a large fraction of the trap volume. Comparison to ab-initio calculations gives excellent agreement with dipolar relaxatio…
