Absolute Ground State Research Articles

Cold and intense OH radical beam sources.

We present the design and performance of two supersonic radical beam sources: a conventional pinhole-discharge source and a dielectric barrier discharge (DBD) source, both based on the Nijmegen pulsed valve. Both designs have been characterized by discharging water molecules seeded in the rare gases Ar, Kr, or Xe. The resulting OH radicals have been detected by laser-induced fluorescence. The measured OH densities are (3.0 ± 0.6) × 10(11) cm(-3) and (1.0 ± 0.5) × 10(11) cm(-3) for the pinhole-discharge and DBD sources, respectively. The beam profiles for both radical sources show a relative longitudinal velocity spread of about 10%. The absolute rotational ground state population of the OH beam generated from the pinhole-discharge source has been determined to be more than 98%. The DBD source even produces a rotationally colder OH beam with a population of the ground state exceeding 99%. For the DBD source, addition of O2 molecules to the gas mixture increases the OH beam density by a factor of about 2.5, improves the DBD valve stability, and allows to tune the mean velocity of the radical beam.

Rashba realization: Raman with RF

We theoretically explore a Rashba spin–orbit coupling scheme which operates entirely in the absolute ground state manifold of an alkali atom, thereby minimizing all inelastic processes. An energy gap between ground eigenstates of the proposed coupling can be continuously opened or closed by modifying laser polarizations. Our technique uses far-detuned ‘Raman’ laser coupling to create the Rashba potential, which has the benefit of low spontaneous emission rates. At these detunings, the Raman matrix elements that link mF magnetic sublevel quantum numbers separated by two are also suppressed. These matrix elements are necessary to produce the Rashba Hamiltonian within a single total angular momentum f manifold. However, the far-detuned Raman couplings can link the three XYZ states familiar to quantum chemistry, which possess the necessary connectivity to realize the Rashba potential. We show that these XYZ states are essentially the hyperfine spin eigenstates of dressed by a strong radio-frequency magnetic field.

Formation of weakly bound molecular complexes: ( $$^3$$ 3 He) $$_2$$ 2

Experimental evidence for low-temperature (exothermic) atom-exchange chemical reactions was recently reported after starting with an optically trapped near-quantum-degenerate gas of polar $$^{40}$$ K $$^{87}$$ Rb (fermionic) molecules prepared in their absolute ground state. Here we demonstrate the similar fermionic ( $$^3$$ He $$^3$$ He) molecules formation via vacancies in quantum $$^4$$ He crystal. A quantum crystal is defined as one in which the energy of the zero-point oscillations of each atom is not small in comparison with the depth of the potential well in which the atom is located (or mathematically $$\Lambda \equiv (\hbar /a\sqrt{m\,E_i})\ge 1$$ ; m is the mass of an atom, $$E_i$$ is the characteristic interaction energy of the atoms, and a is the interatomic distance). Our modified Gross–Pitaevskii approach, based on the extention to Anderson’s adopting Gross–Pitaevskii equation for treating dilute vacancies, supplies in particular the zero-energy limit of the wave function (and the extra energy caused by the curvature of the wave function) for investigations of possible formation of ( $$^3$$ He) $$_2$$ molecules bound by the elastic deformation field around the isotopic impurities as well as bound states (scattering resonances) for a $$^3$$ He-vacancy system in crystalline $$^4$$ He.

Two-photon pathway to ultracold ground state molecules of 23Na40K

We report on high-resolution spectroscopy of ultracold fermionic 23Na40K Feshbach molecules, and identify a two-photon pathway to the rovibrational singlet ground state via a resonantly mixed B1Π ∼ c3Σ+intermediate state. Photoassociation in a 23Na–40K atomic mixture and one-photon spectroscopy on 23Na40K Feshbach molecules reveal about 20 vibrational levels of the electronically excited c3Σ+state. Two of these levels are found to be strongly perturbed by nearby B1Π levels via spin–orbit coupling, resulting in additional lines of dominant singlet character in the perturbed complex , or of resonantly mixed character in . The dominantly singlet level is used to locate the absolute rovibrational singlet ground state via Autler–Townes spectroscopy. We demonstrate coherent two-photon coupling via dark state spectroscopy between the predominantly triplet Feshbach molecular state and the singlet ground state. Its binding energy is measured to be 5212.0447(1) cm−1, a thousand-fold improvement in accuracy compared to previous determinations. In their absolute singlet ground state, 23Na40K molecules are chemically stable under binary collisions and possess a large electric dipole moment of 2.72 Debye. Our work thus paves the way towards the creation of strongly dipolar Fermi gases of NaK molecules.

Molecular beam study of thea3Σ+state of NaK up to the dissociation limit

We provide spectroscopic data for the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state of the $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and driving the population to the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state, using a $\ensuremath{\Lambda}$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\ensuremath{\Pi}/c{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ state from ${v}_{a}=2$ up to the highest vibrational levels for rotational quantum numbers ${N}_{a}=4,6,8$. By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\ensuremath{\Lambda}$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecules from the $\text{Na}(3s)+\text{K}(4s)$ asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state ${v}_{X}=0,J=0$ with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the $\text{Na}(3s)+\text{K}(4p)$ asymptote allows predictions of efficient paths for $^{23}\mathrm{Na}^{40}\mathrm{K}$; one example is calculated.

Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

Finding the ground states of the Ising Hamiltonian [1] maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence, and social network. So far no efficient classical and quantum algorithm is known for these problems, and intensive research is focused on creating physical systems - Ising machines - capable of finding the absolute or approximate ground states of the Ising Hamiltonian [2-6]. Here we report a novel Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections [7]. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programed the smallest non-deterministic polynomial time (NP)- hard Ising problem on the machine, and in 1000 runs of the machine no computational error was detected.

Separating para and ortho water.

Water exists as two nuclear-spin isomers, para and ortho, determined by the overall spin of its two hydrogen nuclei. For isolated water molecules, the conversion between these isomers is forbidden and they act as different molecular species. Yet, these species are not readily separated, and no pure para sample has been produced. Accordingly, little is known about their specific physical and chemical properties, conversion mechanisms, or interactions. The production of isolated samples of both spin isomers is demonstrated in pure beams of para and ortho water in their respective absolute ground state. These single-quantum-state samples are ideal targets for unraveling spin-conversion mechanisms, for precision spectroscopy and fundamental symmetry-breaking studies, and for spin-enhanced applications, for example laboratory astrophysics and astrochemistry or hypersensitized NMR experiments.

Production of optically trappedRbCs87Feshbach molecules

We report the production of $^{87}$RbCs Feshbach molecules in a crossed-beam dipole trap. A mixture of $^{87}$Rb and $^{133}$Cs is cooled close to quantum degeneracy before an interspecies Feshbach resonance at 197\,G is used to associate up to $\sim5000$ molecules with a temperature of $\sim300$\,nK. The molecules are confined in the dipole trap with a lifetime of 0.21(1)\,s, long enough for future experiments exploring optical transfer to the absolute ground state. We have measured the magnetic moment of the Feshbach molecules in a magnetic bias field range between 181 and 185\,G to demonstrate the ability to control the character of the molecular state. In addition we have performed Feshbach spectroscopy in a field range from 0 to 1200\,G and located three previously unobserved resonances at high magnetic fields.

Multichannel modeling and two-photon coherent transfer paths in NaK

We explore possible pathways for the creation of ultracold polar NaK molecules in their absolute electronic and rovibrational ground state starting from ultracold Feshbach molecules. In particular, we present a multi-channel analysis of the electronic ground and K(4p)+Na(3s) excited state manifold of NaK, analyze the spin character of both the Feshbach molecular state and the electronically excited intermediate states and discuss possible coherent two-photon transfer paths from Feshbach molecules to rovibronic ground state molecules. The theoretical study is complemented by the demonstration of STIRAP transfer from the X^1\Sigma^+ (v=0) state to the a^3\Sigma^+ manifold on a molecular beam experiment.

Laser cooling of rotation and vibration by optical pumping

We have recently demonstrated that optical pumping methods combined with photo-association of ultra-cold atoms can produce ultra-cold and dense samples of molecules in their absolute rovibronic ground state. More generally, both the external and internal degrees of freedom can be cooled by addressing selected rovibrational levels on demand. Here, we recall the basic concepts and main steps of our experiments, including the excitation schemes and detection techniques we use to achieve the rovibrational cooling of Cs2 molecules. In addition, we present the determination of formation pathways and a theoretical analysis explaining the experimental observations. These simulations improve the spectroscopic knowledge required to transfer molecules to any desired rovibrational level.

Chlorine atom densities in the excited spin–orbit state measured by two-photon absorption laser-induced fluorescence in a chlorine inductively coupled plasma

Chlorine atom densities in the spin–orbit excited state were measured by two-photon absorption laser-induced fluorescence (TALIF) in an inductively coupled plasma discharge in pure Cl2. The atoms were excited by two photons at 235.702 nm to the state and detected by fluorescence to the (4s) 4P5/2 state at 726 nm. The population of this state relative to that in the ground state, was determined from the relative TALIF signal intensity from the two states, combined with new calculations of the two-photon absorption cross-sections. was found to increase continuously with radio-frequency power (50–500 W), whereas with Cl2 pressure (5–90 mTorr) it passes through a maximum at 10 mTorr, reaching ∼30% at 500 W. This maximum corresponds to the maximum of electron density in the discharge. Combining this density ratio measurement with previous measurements of the absolute ground state chlorine atom density [] allows the absolute spin-orbit excited state density to be estimated. A significant fraction of the total chlorine atom density is in this excited state which should be included in plasma chemistry models.

Resonant optical absorption spectroscopy of Ce

Resonant optical absorption of ground state Ce atoms is demonstrated. Ce I resonant emission line at 461.05 nm (Aij = 28 × 108 s−1) corresponding to the transition 4f5d6s2–4f2(1G)5d (2I)6s is utilized. In a magnetron sputtering discharge used as an atomic source, the absolute densities of atomic ground state Ce sputtered in pure Ar and in Ar–O2 (oxidized magnetron cathode) gas mixtures are found to be nearly 2 × 108 cm−3 (pure Ar) and 1 × 107 cm−3 (Ar + O2). The phenomena inherent in reactive sputtering, such as the non-oxidized–oxidized regime transition and the hysteresis of the transition point, are detected. The obtained data are compared with the existing results of a similar absorption analysis performed in the Ti dc magnetron discharges. The discrepancies in the obtained Ce and Ti absolute ground state densities are analysed.

Strongly interacting Fermi gases

Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.

Effects of N2O and O2 addition to nitrogen Townsend dielectric barrier discharges at atmospheric pressure on the absolute ground-state atomic nitrogen density

Absolute ground-state density of nitrogen atoms N (2p3 4S3/2) in non-equilibrium Townsend dielectric barrier discharges (TDBDs) at atmospheric pressure sustained in N2/N2O and N2/O2 gas mixtures has been measured using Two-photon absorption laser-induced fluorescence (TALIF) spectroscopy. The quantitative measurements have been obtained by TALIF calibration using krypton as a reference gas. We previously reported that the maximum of N (2p3 4S3/2) atom density is around 3 × 1014 cm−3 in pure nitrogen TDBD, and that this maximum depends strongly on the mean energy dissipated in the gas. In the two gas mixtures studied here, results show that the absolute N (2p3 4S3/2) density is strongly affected by the N2O and O2 addition. Indeed, the density still increases exponentially with the energy dissipated in the gas but an increase in N2O and O2 amounts (a few hundreds of ppm) leads to a decrease in nitrogen atom density. No discrepancy in the order of magnitude of N (2p3 4S3/2) density is observed when comparing results obtained in N2/N2O and N2/O2 mixtures. Compared with pure nitrogen, for an energy of ∼90 mJ cm−3, the maximum of N (2p3 4S3/2) density drops by a factor of 3 when 100 ppm of N2O and O2 are added and it reduces by a factor of 5 for 200 ppm, to reach values close to our TALIF detection sensitivity for 400 ppm (1 × 1013 cm−3 at atmospheric pressure).

Rovibrational Cooling of Molecules by Optical Pumping

We demonstrate rotational and vibrational cooling of cesium dimers by optical pumping techniques. We use two laser sources exciting all the populated rovibrational states, except a target state that thus behaves like a dark state where molecules pile up thanks to absorption-spontaneous emission cycles. We are able to accumulate photoassociated cold Cs(2) molecules in their absolute ground state (v = 0, J = 0) with up to 40% efficiency. Given its simplicity, the method could be extended to other molecules and molecular beams. It also opens up general perspectives in laser cooling the external degrees of freedom of molecules.

Time-resolved laser-induced fluorescence diagnostics in a HIPIMS discharge

Laser-induced fluorescence (LIF) combined with resonant optical absorption spectroscopy (ROAS) were utilized for characterization of the Ar-Ti high-power impulse sputtering (HIPIMS) discharge at working pressures of 5 and 20 mTorr. The LIF measurements were performed during the plasma off-time. It was shown that the time-behavior of the measured densities depends strongly on the working pressure in the reactor as well as on the distance from the magnetron target. ROAS measurements indicates that the absolute ground state level density of Ti can reach ≈ 1011 cm−3 (at 20 mTorr, 10 μs pulse, and 12 kW of applied power per pulse). Generally, the obtained results indicate highly non-uniform spatial and temporal behavior of the sputtered species such as Ti and Ti+, which correlate with the results previously obtained in the other magnetron discharges.

Enhanced neutral depletion in a static helium helicon discharge

Laser-induced fluorescence (LIF) measurements of plasma opacity are used as a novel diagnostic to determine the absolute density of a metastable state of neutral helium atoms in a helicon plasma. The absorption scale length at a wavelength of 587.725 nm (vacuum) is determined from measurements of fluorescence intensity as a function of distance along the laser path. With a collisional–radiative model of the state populations, the absolute ground state neutral helium density is estimated from the metastable state density measurement. This paper expands upon previous work through measurements of neutral density, temperature and flow at different radial positions. The measured neutral density decreases by two orders of magnitude from the edge of the plasma to the axis of the plasma source. When the helicon source is operated in a static mode (i.e. no active gas pumping) the on-axis neutral density decreases by 69% from the pumping case and the on-axis plasma density increases by 42%; yielding an ionization fraction of approximately 90%.

Impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

We study the problem of a single impurity of mass $M$ immersed in a Fermi sea of particles of mass $m$. The impurity and the fermions interact through an $s$-wave narrow Feshbach resonance, so that the Feshbach length ${R}_{*}$ naturally appears in the system. We use simple variational ans\"atze, limited to at most one pair of particle-hole excitations of the Fermi sea, and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed-channel population which is experimentally accessible. Finally, we identify a nontrivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.

Femtosecond pulses and dynamics of molecular photoexcitation: RbCs example

We investigate the dynamics of molecular photoexcitation by unchirped femtosecond laser pulses using RbCs as a model system. This study is motivated by a goal of optimizing a two-color scheme of transferring vibrationally-excited ultracold molecules to their absolute ground state. In this scheme the molecules are initially produced by photoassociation or magnetoassociation in bound vibrational levels close to the first dissociation threshold. We analyze here the first step of the two-color path as a function of pulse intensity from the low-field to the high-field regime. We use two different approaches, a global one, the 'Wavepacket' method, and a restricted one, the 'Level by Level' method where the number of vibrational levels is limited to a small subset. The comparison between the results of the two approaches allows one to gain qualitative insights into the complex dynamics of the high-field regime. In particular, we emphasize the non-trivial and important role of far-from-resonance levels which are adiabatically excited through 'vertical' transitions with a large Franck-Condon factor. We also point out spectacular excitation blockade due to the presence of a quasi-degenerate level in the lower electronic state. We conclude that selective transfer with femtosecond pulses is possible in the low-field regime only. Finally, we extend our single-pulse analysis and examine population transfer induced by coherent trains of low-intensity femtosecond pulses.

Feshbach resonances in an ultracold mixture of 87Rb and 40K

We report the experimental preparations of the absolute ground states of 87Rb and 40K atoms (|F = 1, mF = 1〉 + |F = 9/2, mF = −9/2〉) by means of the radio-frequency and microwave adiabatic rapid passages, and the observation of magnetic Feshbach resonances in an ultracold mixture of bosonic 87Rb and fermionic 40K atoms between 0 T and 6.0 × 10−2 T, including 7 homonuclear and 4 heteronuclear Feshbach resonances. The resonances are identified by the abrupt trap loss of atoms induced by the strong inelastic three-body collisions. These Feshbach resonances should enable the experimental control of interspecies interactions.