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We describe the design and performance of a large magnetic trap for storing and cooling of atomic hydrogen (H). The trap operates in the vacuum space of a dilution refrigerator at a temperature of 1.5 K. Aiming at a large volume of the trap we implemented the octupole configuration of linear currents (Ioffe bars) for the radial confinement, combined with two axial pinch coils and a 3 T solenoid for the cryogenic H dissociator. The octupole magnet consists of eight race-track segments which are compressed towards each other with magnetic forces. This provides a mechanically stable and robust construction with a possibility of replacement or repair of each segment. A maximum trap depth of 0.54 K (0.8 T) was reached, corresponding to an effective volume of 0.5 liters for hydrogen gas at 50 mK. This is an order of magnitude larger than ever used for trapping atoms.

We present an experimental study of the Dynamic Nuclear Polarization (DNP) of \si{} nuclei in silicon crystals of natural abundance doped with As in the temperature range 0.1-1 K and in strong magnetic field of 4.6 T. This ensures very high degree of electron spin polarization, extremely slow nuclear relaxation and optimal conditions for realization of Overhauser and resolved solid effects. We found that the solid effect DNP leads to an appearance of a pattern of holes and peaks in the ESR line, separated by the super-hyperfine interaction between the donor electron and \si{} nuclei closest to the donor. On the contrary, the Overhauser effect DNP mainly affects the remote \si{} nuclei having the weakest interaction with the donor electron. This leads to an appearance of a very narrow ($\approx$ 3 mG wide) hole in the ESR line. We studied relaxation of the holes after burning, which is caused by the nuclear spin diffusion. Analyzing the spin diffusion data with a simple one-dimensional spectral diffusion model leads to a value of the spectral diffusion coefficient $D=8(3)\times 10^{-3}$ mG$^2$/s. Our data indicate that the spin diffusion is not completely prevented even in the frozen core near the donors. The emergence of the narrow hole after the Overhauser DNP may be explained by a partial "softening" of the frozen core caused by Rabi oscillations of the electron spin., Comment: 10 pages, 10 figures

Our recent experimental work on electron spin waves in atomic hydrogen gas has prompted a revisit of the theory of the Identical Spin Rotation Effect (ISRE). A key characteristic determining the properties of the spin waves is the quality factor of ISRE. Unfortunately, calculating this quality factor takes some toil. In this paper we summarize some results of the ISRE theory in dilute gases. We also derive asymptotic formulae for the quality factor and examine their accuracy for hydrogen and $^3$He., Comment: 13 pages, 3 figures

We present the results of experiments on dynamic nuclear polarization and relaxation of 75As in silicon crystals. Experiments are performed in strong magnetic fields of 4.6 T and temperatures below 1 K. At these conditions donor electron spins are fully polarized, and the allowed and forbidden ESR transitions are well resolved. We demonstrate effective nuclear polarization of 75As nuclei via the Overhauser effect on the time scale of several hundred seconds. Excitation of the forbidden transitions leads to a polarization through the solid effect. The relaxation rate of donor nuclei has strong temperature dependence characteristic of Orbach process., Comment: 9 pages, 7 figures

We report on a study of Dynamic Nuclear Polarization and electron and nuclear spin relaxation of atomic hydrogen and deuterium in solid molecular matrices of H$_{2}$, D$_{2}$, and HD mixtures. The electron and nuclear spin relaxation times ($T_{1e}$ and $T_{1N}$) were measured within the temperature range 0.15-2.5$\,$K in a magnetic field of 4.6 T, conditions which ensure a high polarization of electron spins. We found that $T_{1e}$ is nearly temperature independent in this temperature range, while $T_{1N}$ decreased by 2 orders of magnitude. Such strong temperature dependence is typical for the nuclear Orbach mechanism of relaxation via the electron spins. We found that the nuclear spins of H atoms in solid D$_{2}$ and D$_{2}:$HD can be efficiently polarized by the Overhauser effect. Pumping the forbidden transitions of H atoms also leads to DNP, with the efficiency strongly dependent on the concentration of D atoms. This behaviour indicates the Cross effect mechanism of the DNP and nuclear relaxation, which turns out to be well resolved in the conditions of our experiments. Efficient DNP of H atoms was also observed when pumping the middle D line located in center of the ESR spectrum. This phenomenon can be explained in terms of clusters or pairs of H atoms with strong exchange interaction. These clusters have partially allowed transitions in the center of the ESR spectrum and DNP may be created via the resolved Cross effect.

We present an experimental study of electron spin waves in atomic hydrogen gas compressed to high densities of $\sim 5 \times 10^{18}$ cm$^{-3}$ at temperatures ranging from 0.26 to 0.6 K in strong magnetic field of 4.6 T. Hydrogen gas is in a quantum regime when the thermal de Broglie wavelength is much larger than the s-wave scattering length. In this regime the identical particle effects play major role in atomic collisions and lead to the Identical Spin Rotation effect (ISR). We observed a variety of spin wave modes caused by this effect with strong dependence on the magnetic potential caused by variations of the polarizing magnetic field. We demonstrate confinement of the ISR modes in the magnetic potential and manipulate their properties by changing the spatial profile of magnetic field. We have found that at a high enough density of H gas the magnons accumulate in their ground state in the magnetic trap and exhibit long coherence, which has a profound effect on the electron spin resonance spectra. Such macroscopic accumulation of the ground state occurs at a certain critical density of hydrogen gas, where the chemical potential of the magnons becomes equal to the energy of their ground state in the trapping potential., Comment: 16 pages, 15 figures

We report on the first ESR study of atomic hydrogen and tritium stabilized in a solid T$_{2}$ and T$_{2}$:H$_{2}$ matrices down to 70$\,$mK. The concentrations of T atoms in pure T$_{2}$ approached $2\times10^{20}$cm$^{-3}$ and record-high concentrations of H atoms $\sim1\times10^{20}$cm$^{-3}$ were reached in T$_{2}$:H$_{2}$ solid mixtures where a fraction of T atoms became converted into H due to the isotopic exchange reaction T+H$_2\rightarrow$TH+H. The maximum concentrations of unpaired T and H atoms was limited by their recombination which becomes enforced by efficient atomic diffusion due to a presence of a large number of vacancies and phonons generated in the matrices by $\beta$-particles. Recombination also appeared in an explosive manner both being stimulated and spontaneously in thick films where sample cooling was insufficient. We suggest that the main mechanism for H and T migration is physical diffusion related to tunneling or hopping to vacant sites in contrast to isotopic chemical reactions which govern diffusion of H and D atoms created in H$_{2}$ and D$_{2}$ matrices by other methods.

We report on a study of the exchange tunneling reaction D+HD$\rightarrow$D$_{2}$+H in a pure solid HD matrix and in a D$_{2}$ matrix with 0.23$\%$ HD admixture at temperatures between 130$\,$mK and 1.5$\,$K. We found that the exchange reaction rates, $k_{exHD}\sim3\times10^{-27}$cm$^{3}$s$^{-1}$ in the pure HD matrix, and $k_{exD_{2}}=9(4)\times10^{-28}$cm$^{-3}$ in the D$_{2}$ matrix are nearly independent of temperature within this range. This confirms quantum tunnelling nature of these reactions, and their ability to proceed at temperatures down to absolute zero. Based on these observations we concluded that exchange tunneling reaction H+H$_{2}\rightarrow$H$_{2}$+H should also proceed in a H$_{2}$ matrix at the lowest temperatures. On contrary, the recombination of H atoms in solid H$_{2}$ and D atoms in solid D$_{2}$ is substantially suppressed at the lowest temperatures as a result of increasing of violation for resonance tunneling of atoms when they approach each other.

We report on experimental observation of BEC-like behaviour of quantized electron spin waves (magnons) in a dense gas of spin polarized atomic hydrogen. The magnons are trapped and controlled with inhomogeneous magnetic fields, and described by a Schr\"odinger-like wave equation, in analogy to the BEC experiments with neutral atoms. We have observed the appearance of a sharp feature in the ESR spectrum displaced from the normal spin wave spectrum. We believe that this observation corresponds to a sudden growth of the ground state population of the magnons and emergence of their spontaneous coherence for hydrogen gas densities exceeding a critical value, dependent on the trapping potential. We interpret the results as a BEC of non-equilibrium magnons which were formed by applying the rf power., Comment: 5 pages, 3 figures Supplemental material: 3 pages, 3 figures. Accepted for publication in Physical Review Letters

We demonstrate an efficient control of $^{29}$Si nuclear spin orientation for specific lattice sites near $^{31}$P donors in silicon crystals at temperatures below 1 K and in high magnetic field of 4.6 T. Excitation of the forbidden electron-nuclear transitions leads to a pattern of narrow holes and peaks in the ESR lines of $^{31}$P. The pattern originates from dynamic polarization the $^{29}$Si nuclear spins near the donors via the solid effect. This method can be used for initialization of qubits based on $^{29}$Si nuclear spins in the all-silicon quantum computer. In comparison, polarization of $^{29}$Si performed by pumping the allowed ESR transitions, did not create any patterns. Instead, a single narrow spectral hole was burnt in the ESR line. The difference is explained by a rapid spin diffusion during the microwave pumping of the allowed transitions.

We demonstrate that the dynamic nuclear polarization (DNP) of phosphorus donors in silicon can be very effective in a magnetic field of 4.6 T and at temperatures below 1 K. The DNP occurs due to the Overhauser effect following a cross relaxation via the forbidden flip-flop or flip-flip transitions. Nuclear polarization values $P>0.98$ were reached after 20 min of pumping with 0.4 $\mu$W of microwave power. We evaluated that the ratio of hyperfine state populations increased by three orders of magnitude after 2 hours of pumping, and an extremely pure nuclear spin system containing $<10^{-11}$ of the other spin state can be created. An inverted DNP has been obtained by pumping the low field ESR line of P followed by the flip-flip cross relaxation. This transition has much smaller relaxation rate and required substantially longer pumping times. We found that the nuclear polarization dynamics deviates substantially from a simple exponential function. The evolution of the polarization is characterized by two time constants $T^{'}_{ac}\approx$15 s in the beginning, and $T^{"}_{ac}\approx$1100 s for long pumping time. Temperature dependence of the nuclear relaxation rate of $^{31}$P was studied down to 0.75 K, below which the relaxation time became too long to be measured. The nuclear polarization followed a bi-exponential time dependence during relaxation. We suggest that the non-exponential behavior of DNP dynamics and the subsequent relaxation is mediated by the nuclei of $^{29}$Si surrounding $^{31}$P donors, which affect the transition probabilities of the forbidden cross-relaxation processes.

We present a high magnetic field study of electron spin waves in atomic hydrogen gas compressed to high densities of 10^18 cm^-3 at temperatures ranging from 0.26 to 0.6 K. We observed a variety of spin wave modes caused by the identical spin rotation effect with strong dependence on the spatial profile of the polarizing magnetic field. We demonstrate confinement of these modes in regions of strong magnetic field and manipulate their spatial distribution by changing the position of the field maximum., Comment: 5 pages, 4 figures

We describe experiments with spin-polarized atomic hydrogen gas adsorbed on liquid $^{4}$He surface. The surface gas density is increased locally by thermal compression up to $5.5\times10^{12}$ cm$^{-2}$ at 110 mK. This corresponds to the onset of quantum degeneracy with the thermal de-Broglie wavelength being 1.5 times larger than the mean interatomic spacing. The atoms were detected directly with a 129 GHz electron-spin resonance spectrometer probing both the surface and the bulk gas. This, and the simultaneous measurement of the recombination power, allowed us to make accurate studies of the adsorption isotherm and the heat removal from the adsorbed hydrogen gas. From the data, we estimate the thermal contact between 2D hydrogen gas and phonons of the helium film. We analyze the limitations of the thermal compression method and the possibility to reach the superfluid transition in 2D hydrogen gas., Comment: 20 pages, 11 figures

We report a measurement of the cold collision frequency shift in atomic hydrogen gas adsorbed on the surface of superfluid 4He at T<=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 v_c = -1.0(1)x10^-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 3D case., Comment: 4 pages, 3 figures