Two-dimensional Atomic Hydrogen Research Articles

Interaction-enhanced double resonance in cold gases

A new type of double-resonance spectroscopy of a quantum gas based on interaction-induced frequency modulation of a probe transition has been considered. Interstate interaction of multilevel atoms causes a coherence-dependent collisional shift of the transition between the atomic states |1> and |2> due to a nonzero population of the state |3>. Thus, the frequency of the probe transition |1>-|2> experiences oscillations associated with the Rabi oscillations between the states |1> and |3> under continuous excitation of the drive resonance |1>-|3>. Such a dynamic frequency shift leads to a change in the electromagnetic absorption at the probe frequency and, consequently, greatly enhances the sensitivity of double-resonance spectroscopy as compared to traditional "hole burning", which is solely due to a decrease in the population of the initial state |1>. In particular, it has been shown that the resonance linewidth is determined by the magnitude of the contact shift and the amplitude of the drive field and does not depend on the static field gradient. The calculated line shape and width agree with the low-temperature electron-nuclear double-resonance spectra of two-dimensional atomic hydrogen.

Nature of a nonzero frequency shift of a hyperfine transition in two-dimensional atomic hydrogen

We propose the explanation of a surprisingly small hyperfine frequency shift in the two-dimensional (2D) atomic hydrogen bound to the surface of superfluid helium below 0.1 K. Owing to the symmetry considerations, the microwave-induced triplet-singlet transitions of atomic pairs in the fully spin-polarized sample are forbidden. The apparent nonzero shift is associated with the density-dependent wall shift of the hyperfine constant and the pressure shift due to the presence of H atoms in the hyperfine state $a$ not involved in the observed $b\to c$ transition. The interaction of adsorbed atoms with one another effectively decreases the binding energy and, consequently, the wall shift by the amount proportional to their density. The pressure shift of the $b\to c$ resonance comes from the fact that the impurity $a$-state atoms interact differently with the initial $b$-state and final $c$-state atoms and is also linear in density. The net effect of the two contributions, both specific for 2D hydrogen, is comparable with the experimental observation. To our knowledge, this is the first mentioning of the density-dependent wall shift. We also show that the difference between the triplet and singlet scattering lengths of H atoms, $a_t-a_s=30(5)$ pm, is exactly twice smaller than the value reported by Ahokas {\it et al.}, Phys. Rev. Lett. {\bf101}, 263003 (2008).

Magnetic Resonance Studies of Cold Atomic Hydrogen Gas

We present magnetic resonance studies of two-dimensional atomic hydrogen gas (H↓) in 4.6 T field at temperatures 70–100 mK i.e. well in the quantum gas or cold collision regime. Electron spin resonance at 128 GHz and nuclear magnetic resonance at 910 MHz were used to detect and manipulate populations of the hyperfine manifold of the electronic ground state. Using a coherent two-photon excitation we demonstrated effects of electromagnetically induced transparency and absorption as well as coherent population trapping in the 2D H gas. We performed a measurement of the magnetic resonance line shifts associated with exchange and dipolar interactions. The cold collision (clock) shift measured for the 2D case is two orders of magnitude smaller than predicted by the mean field theory and is of the same order as the internal dipolar field.

Cold Collision Frequency Shift in Two-Dimensional Atomic Hydrogen

We report a measurement of the cold collision frequency shift in atomic hydrogen gas adsorbed on the surface of superfluid (4)He at T approximately < 90 mK. Using two-photon electron and nuclear magnetic resonance in 4.6 T field we separate the resonance line shifts due to the dipolar and exchange interactions, both proportional to surface density sigma. We find the clock shift Delta nu(c) = -1.0(1) x 10(-7) Hz cm(-2) x sigma, which is about 100 times smaller than the value predicted by the mean field theory and known scattering lengths in the three-dimensional case.

Coherence and recombination in two-dimensional atomic hydrogen on the surface of superfluid 4He

Experimental results on the achievement of high degrees of quantum degeneration in two-dimensional atomic hydrogen (2D H↓) by the magnetic-compression method are analyzed by taking into account current data on the binding energy Ea = 1.14(1) K of hydrogen atoms with the 4He surface and the constant Kab of the two-particle exchange recombination of adsorbed H atoms. The behavior of pair and three-particle correlation functions, as well as the transverse delocalization of the wavefunction of adsorbed atoms due to their interaction with each other, is taken into account self-consistently. A new mechanism of cooling of the compression region by means of the flow of H atoms on the helium surface with the subsequent evaporation and emission from a magnetic trap is proposed. This mechanism prevails at high densities, whereas the heat transfer at low densities occurs owing mainly to the interaction of ripplons with the phonons of the helium film. Existing data corroborate the achievement of the phase density σλ2 ≳ 10, which is certainly higher than the density necessary for both the arrangement of local coherence in 2D H↓ and its transition to the superfluid state. The results agree with the representations on quasi-condensation; however, direct evidence of this phenomenon is not revealed. The probability of three-particle dipole recombination that is corrected for the quantum correlation and delocalization is equal to 7(2) × 10−26 cm4 s−1 (T = 0.15, …, 0.21 K, B = 6.6 T, and σλ2 = 1, …, 9). The results are compared with other theoretical and experimental data.

Three-body recombination in two-dimensional atomic hydrogen gas

We study three-body recombination in the gas of spin-polarized atomic hydrogen adsorbed on the surface of superfluid helium at temperatures from $45\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}130\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. The two-dimensional gas is thermally compressed to densities up to $\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ using the ``cold spot'' method which makes the three-body process the dominant decay channel in the system. We measure the loss rate and surface density of atoms directly and independently and observe the former to be proportional to the third power of the latter. The result for the surface three-body recombination rate constant at $4.6\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, ${L}_{s}=2.0(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$, significantly reduces the discrepancy between the theory and earlier measurements where the surface density was inferred from the adsorption isotherm. We also measured the three-body rate constant on a 0.1% $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ film and found ${L}_{s}=1.3(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$. This larger value is attributed to an increased delocalization of adsorbed hydrogen atoms in the direction normal to the surface.

Thermal compression of two-dimensional atomic hydrogen gas

We describe experiments where two-dimensional (2D) atomic hydrogen gas is compressed thermally at a small ``cold spot'' on the surface of superfluid helium and detected directly with electron-spin resonance. We reach surface densities up to $5\ifmmode\times\else\texttimes\fi{}{10}^{12}{\mathrm{cm}}^{\ensuremath{-}2}$ at temperatures $\ensuremath{\approx}100\mathrm{mK}$ corresponding to the maximum 2D phase-space density $\ensuremath{\approx}1.5.$ By independent measurements of the surface density and its decay rate we make a direct determination of the three-body recombination rate constant and get the upper bound ${L}_{3b}\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}{\mathrm{cm}}^{4}/\mathrm{s}$ which is an order of magnitude smaller than previously reported experimental results.

Electron-spin-resonance instability in two-dimensional atomic hydrogen gas.

We study by electron-spin-resonance spin-polarized atomic hydrogen adsorbed on the surface of superfluid helium at temperatures T(S) from 50 to 110 mK. The average dipolar field in this 2D system shifts the electron-spin-resonance peak of the adsorbed atoms relative to that of bulk atoms. The shift is directly proportional to surface density. The role of longitudinal magnetization relaxation is played by particle exchange between the 2D and the 3D phases, which diminishes exponentially with decreasing T(S). Therefore at T(S) less, similar 80 mK an excitation field of 0.1 mG disturbs the equilibrium surface density and leads to a magnetization instability observed as sawtooth shaped resonance lines.

Low dimensional Bose gases

We present an improved many-body T-matrix theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. The resulting mean-field theory is valid in arbitrary dimensions and able to describe the low-temperature crossover between three, two and one-dimensional Bose gases. When applied to a degenerate two-dimensional atomic hydrogen gas, we obtain a reduction of the three-body recombination rate which compares favorably with experiment. Supplementing the mean-field theory with a renormalization-group approach to treat the critical fluctuations, we also incorporate into the theory the Kosterlitz-Thouless transition that occurs in a homogeneous Bose gas in two dimensions. In particular, we calculate the critical conditions for the Kosterlitz-Thouless phase transition as a function of the microscopic parameters of the theory. The proposed theory is further applied to a trapped one-dimensional Bose gas, where we find good agreement with exact numerical results obtained by solving a nonlinear Langevin field equation.

Two-dimensional atomic hydrogen concentration maps in hot-filament diamond-deposition environment

This paper reports the two-dimensional mapping of atomic hydrogen concentration with two-photon excited laser induced fluorescence in a multi-wire grid hot-filament chemical vapor deposition reactor. The measurements were made in a diamond film deposition environment under different filament temperatures and wire configurations. The measurement was calibrated with a titration reaction using NO2 as a titrant. The kinetic gas temperature in the reactor was measured from the Doppler broadening of the Lyman-β transition excited in the fluorescence. The filament temperature was found to have a significant effect on atomic hydrogen production and transfer to the substrate. The axial concentration distributions were compared to a one-dimensional kinetic gas–surface chemistry model with good agreement. The model produced a reasonable estimate for the bulk diamond film growth rate.

Local Bose condensate: observations on two-dimensional atomic hydrogen

We report on new experiments at Turku where two-dimensional atomic hydrogen gas has been compressed magnetically to high degrees of quantum degeneracy on the surface of liquid 4He at about 200 mK. The results are in good agreement with our earlier observations: The probability of 3-body dipolar recombination is found to decrease gradually by an order of magnitude but to show no levelling yet, when the 2D phase-space density increases from 3 to 9. This effect is attributed mainly to a decrease in the local 3-particle correlator caused by the appearance and growth of a more or less local 2D condensate. The roles of interactions and out-of-plane delocalization of adsorbed H atoms are also discussed.

Observation of Quasicondensate in Two-Dimensional Atomic Hydrogen

Observation of Quasicondensate in Two-Dimensional Atomic Hydrogen

A practical guide to the next-to-leading order of the perturbation expansion: M. A. Nowak and M. Praszałowicz, Institute of Physics, Jagellonian University, Cracow, Poland; and W. Słominski, Max Planck-Institut für Physick und Astrophysik, Werner Heisenberg-Institute für Physik, D-8000 Munich 40, Federal Republic of Germany

We report on new experiments at Turku where two-dimensional atomic hydrogen gas has been compressed magnetically to high degrees of quantum degeneracy on the surface of liquid 4He at about 200 mK. The results are in good agreement with our earlier observations: The probability of 3-body dipolar recombination is found to decrease gradually by an order of magnitude but to show no levelling yet, when the 2D phase-space density increases from 3 to 9. This effect is attributed mainly to a decrease in the local 3-particle correlator caused by the appearance and growth of a more or less local 2D condensate. The roles of interactions and out-of-plane delocalization of adsorbed H atoms are also discussed.

Scattering length and effective range for scattering in a plane and in higher dimensions

The concepts of scattering length and effective range for low-energy scattering are introduced for general dimension n in such a way that previously encountered dimensional and discontinuity problems are avoided. The theory is applied to two-body scattering in two-dimensional atomic hydrogen gas adsorbed to a superfluid helium film.