Magnetic resonance in Dense Atomic Hydrogen Gas S. Vasiliev of ,

Turku Magnetic resonance in Dense Atomic Hydrogen Gas Sergey Vasiliev University of Turku

H group at Turku:

Janne Ahokas Otto Vainio Ville Virtanen Sergey Sheludyakov Denis Zvezdov*

*also at , Kazan, Russia Why to study H gas?

- The only gas at T=0 - Bose-Einstein Condensation - H-H interactions, cold collisions - Magnetic resonance - Spin waves, BEC of magnons Basic parameters n =−1017 10 18 cm− 3 T =100− 500 mK B ≈ 4.6 T 1 1 ⎛⎞217.4Åπ 22 Λ= ≈ λ0 =≤2 0.1 mm th ⎜⎟ 4π an ⎝⎠mkB T T

Λ≈th 36Å at T =0.3 K aS ≈ 0.72Å

Quantum gas limit

Λ≥th a Λ Onset of quantum degeneracy th

3 nΛth ∼ 1 Cold collisions, Spin waves Spin waves in quantum gases

V. P. Silin, JETP 6,945 (1958) liquid 3He A.J. Legett and M.J. Rice, PRL, 20, 586 (1968) E.P. Bashkin, JETP Lett. 33, 11 (1981) spin-polarized gases C. Lhuillier and F. Laloe, J. Phys (Paris) 43, 197 (1982)

Λth μ ∼ >>1 1 a 2

21

iϕ1 iϕ 2 0 BA ↓+↑=Ψ Ae Be ↓+↑=Ψ

Identical Spin Rotation Effect (ISR) Nuclear spin waves in H↓ gas

Pulsed NMR, spectra after FT D.M. Lee at Cornell University

B. R. Johnson et al., PRL 52, 1508 (1984) Basic equations of ISR spin waves

C. Lhuillier and F. Laloe, J. Phys (Paris) 43, 197 (1982)

+ += iMMM yx

∂−Mi1 εμM + =−iBMDγδ + z ∇2 M ∂+tM00+ 1 μ 22 +

ε =±1 for bosons/fermions D0 – spin diffusion coefficient in unpolarized gas Λ μ ∼ th - spin wave quality factor a iM+ με T ω()kD=− z k22∼ k 0 1+ μ 22M n Schrödinger type equation: Λ μ ∼ th >>1 ∂M D ε iMB+ =∇+0 2 γδ M a ∂t μ + 0 +

M + MMz ≈ kinetic potential Particle εγμ 3He -1 negative neg/pos H +1 positive negative proton H +1 negative, negative electron large

μ Low field seekers High field seekers mn∗ = −−∼ μ ε D0 Calculations of μ for H and 3He

C. Lhuillier, J. Physique 44, 1-12 (1983) Experimental setup

100 μm

B≈4.6 T T=0.2-0.5K

n~1015 cm-3 n→1018 cm-3 Sample lifetime ~3-100 min Compression region

300 nm gold layer 12 μm polyimide (Kapton) film 80 μm Epoxy H↓ gas

3 μm polyimide wall (tube) 4He coolant

mS, mI ½, ½ ½, -½

F=1

F=0 Doubly polarized H gas -½, -½ -½, ½

a + a + M = H + M hyperfine state 2 selective a + b + M = H2 + M recombination: b + b + b = H2 + b CW spectra in static field of optimized homogeneity

4 75 mG

2

0 ESR absorption ESR

-2

-4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Sweep, V [0.39 G/V] Large positive gradient ~40G/cm B(z)

H↓ z gas

0 1 2 G Large negative gradient ~40G/cm B(z) 3

2

H↓ 1 z gas

0

-1

1 G

-2

-3

-2.0 -1.5 -1.0 -0.5 0.0 0.5 Magnetic field sweep, V (@0.4G/V) CW spectra in static field of optimized homogeneity

D ω = 0 k 2 μ 4 H↓ 75 mG 2 π π kn== gas λ L 2

0 π D absorption ESR Δ≤ω 0 ≈1.5 kHz μ L2 ≈0.5 mG

For L=0.5 mm -2 n=1017 cm-3

-4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Sweep, V [0.39 G/V] Large positive gradient ~40G/cm, CW U(z)

H↓ z gas

⎛⎞z 22 itω M + =+Jr0 ()κλAi⎜⎟kz e ⎝⎠λ

1/3 2 μ ω ⎛⎞D κ = λ = 0 D ⎜⎟ 0 ⎝⎠γμezG Large negative gradient ~40G/cm U(z) 3

2

H↓ 1 gas

z 0

-1

⎛⎞z 22 itω M + =+Jr0 ()κλAi⎜⎟kz e ⎝⎠λ -2 1 G 1/3 2 μ ω ⎛⎞D κ = λ = 0 D ⎜⎟ 0 ⎝⎠γμezG -3

-2.0 -1.5 -1.0 -0.5 0.0 0.5 Magnetic field sweep, V (@0.4G/V) T=360 mK

Fit result: μ≈8 ESR spectra with no gradients applied

Is the observed lineshape caused by main ESR peak inhomogeneity of RF field plus the static field inhomogeneity?

magnon peak

-1.0 -0.5 0.0 0.5 1.0 Sweep, G Spectra in various gradients

I = -3A

I = -2A

I = -1A

I = 0A 0.00

-0.05

-0.10 I = +1A

-0.15

-0.20

Peak V (3.8G/V) position, I = +2A -0.25

-0.30 -1.5 -1.0 -0.5 0.0 0.5 SR coil current, Amps I = +3A

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Sweep [V ] (0.78 G/V) Static magnetic field profile, no gradients applied

Epoxy 4π M ≈− 0.8 G Moving trap position with applied gradients Particle in a box + parabolic potential ∂M D ε iMH+ =∇+0 2 γδ M ∂t μ + 0 +

Δω

1 Δω ∼ μn

024681012 Magnetic field, mG 17 −3 n =⋅510 cm , μ =5 -1.0 -0.5 0.0 0.5 1.0 Sweep, G density increases CW spectra,nogradapplied ≈ 10 mG 0.1G Magnetic field orfrequency nc increases at higher T and shallower trap

nc Free Induction Decay

0.020

0.015 Precession frequency does not depend on time

0.010 f ≈130 GHz

FID signal 0.005

6 0.000 Q ≈⋅510 τ~5 s at 1 MHz -0.005 0 5000 10000 15000 20000 25000 30000 35000 40000 time, ns Conclusions

ƒ Spin-polarized H gas is a rich system where a large number of magnetic excitations (magnons) can be studied by means of magnetic resonance.

ƒ We identified four basic types of magnon modes, distinguished by their behavior in magnetic field gradient, at different densities, sample shapes and gas temperatures.

ƒ Applying negative axial magnetic field gradients we observed magnon modes of exchange origin, caused by the ISR effect. These modes do not depend on the sample shape, and are not pure standing waves.

ƒ We found a spectrum of magnon modes trapped in the magnetic field maximum. At high enough gas densities we observed excessive occupation of the ground state in this trap, with long coherent precession of magnetization, similar to the HPD in experiments with liquid 3He.