Ultrafast non-equilibrium dynamics of rotons in superuid helium A.A. Milner1P.C.E. Stamp1 2 3and V. Milner1 1Department of Physics and Astronomy University of British Columbia

2025-05-06 0 0 577.92KB 6 页 10玖币

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Ultrafast non-equilibrium dynamics of rotons in superﬂuid helium

A.A. Milner,1P.C.E. Stamp,1, 2, 3 and V. Milner1

1Department of Physics and Astronomy, University of British Columbia,

6224 Agricultural Rd., Vancouver, B.C., Canada V6T 1Z1

2Theoretical Astrophysics, Cahill, California Institute of Technology,

1200 E. California Boulevard, MC 350-17, Pasadena CA 91125, USA

3Paciﬁc Institute of Theoretical Physics, University of British Columbia,

6224 Agricultural Rd., Vancouver, B.C., Canada V6T 1Z1

Superﬂuid 4He, the ﬁrst superﬂuid ever discov-

ered [1, 2], is in some ways the least well un-

derstood. Unlike 3He superﬂuid [3, 4], or the

variety of Bose-Einstein condensates of ultracold

gases [5, 6], superﬂuid 4He is a very dense liquid

of strongly interacting quasiparticles. The the-

ory [7–9] is then necessarily phenomenological:

the quasiparticle properties are found from ex-

periment, and controversies over their description

still remain, notably regarding vortex dynamics

[10–13] and the nature of rotons and roton pair

creation [14]. It is therefore important to develop

new experimental tools for probing the system far

from equilibrium. Here we describe a method for

locally perturbing the density of superﬂuid he-

lium through the excitation of roton pairs with

ultrashort laser pulses. By measuring the time

dependence of this perturbation, we track the

non-equilibrium evolution of the two-roton states

on a picosecond timescale. Our results reveal an

ultrafast cooling of hot roton pairs as they ther-

malize with the colder gas of other quasiparticles.

We anticipate that these ﬁndings, as well as fu-

ture applications of the introduced ultrafast laser

technique to diﬀerent temperature and pressure

regimes in bulk liquid 4He, will stimulate fur-

ther experimental and theoretical investigations

towards better understanding of superﬂuidity.

The dispersion of the known collective excitations in

superﬂuid 4He, ﬁrst proposed by Landau [15, 16], exhibits

both (i) a single quasiparticle branch with phonon char-

acter at low energy, turning over to maxons and rotons at

higher energy [8]; and (ii) a variety of multi-quasiparticle

excitations, including phonon pairs, hybridized phonon-

roton excitations, roton pairs [17, 18], and even bound

roton triplets [19]. Neutron scattering [20] and sponta-

neous Raman scattering [21–24] give direct evidence for

some of these quasiparticles. In the case of roton pairs,

Raman spectra provide key information about their prop-

erties, such as the two-roton binding energy and lifetime

in the thermal equilibrium state. On the other hand,

the non-equilibrium quasiparticle dynamics and their ap-

proach to equilibrium are largely unknown, despite being

critical for understanding the quasiparticles and their in-

teractions. To the best of our knowledge, here we report

the ﬁrst experimental time-resolved study of roton dy-

namics in superﬂuid helium.

In our experiment (see Methods for details), linearly

polarized infrared femtosecond pulses are focused in the

bulk liquid helium 4He, condensed in a custom-built op-

tical cryostat and cooled below the transition to superﬂu-

idity (the so-called “lambda point” Tλ). The interaction

of the laser ﬁeld E(r) with the ﬂuid can be described by

the Hamiltonian [25]

Hint =−Zd3rρ(r)·µind(r)E(r),(1)

in which µind(r) is the dipole moment induced at the

point rby the same ﬁeld distributed over the interaction

volume (points r0):

µind(r) = Zd3r0ρ(r0)ˆα(r,r0)E(r0).(2)

Here ρ(r) is the density and ˆα(r,r0) is the polarizability

tensor of the ﬂuid. Owing to the dependence of the latter

on the absolute value |r−r0|[25], this interaction results

in an anisotropic re-distribution of the ﬂuid density, and

a corresponding optical birefringence, whose optical axis

is parallel to the polarization vector of the applied elec-

tromagnetic ﬁeld.

We detect the laser(pump)-induced birefringence by

measuring the change in polarization of a much weaker

probe pulse, sent trough the liquid along the same optical

path. As a function of the pump-probe delay, the bire-

fringence signal oscillates at the frequency corresponding

to the energy of a roton pair allowing us for the ﬁrst

time to follow the dynamics of the initially created den-

sity perturbation in the superﬂuid.

We note that an excited roton pair carries very little

translational momentum [26] and two units of angular

momentum [27]. Considering linearly polarized laser ﬁeld

as a superposition of two circularly polarized components

of opposite handedness, the interaction of the ﬁeld with

the superﬂuid can also be described as a stimulated Ra-

man process, in which the absorption of one circular com-

ponent is accompanied by the emission of the other. In

this regard, the observed phenomenon is analogous to the

Raman-induced Kerr eﬀect [28], widely used in molecular

spectroscopy [29]. Crucially, the stimulated mechanism

of interaction provides a unique opportunity to track only

those roton pairs excited by the pump pulse, rather than

sampling all quasiparticles in the interaction volume (as

would be the case in spontaneous Raman scattering).

arXiv:2210.05374v1 [cond-mat.quant-gas] 9 Oct 2022

FIG. 1. Laser-induced optical birefringence of superﬂuid he-

lium at T= 1.38(2) K and saturated vapor pressure. The raw

experimental data is shown in (a). In (b), the power spec-

trum of the experimental signal is calculated with a Fourier

transform (red asterisks) and ﬁtted to a Lorentzian (solid

black line). The details of the resonant peak are shown in

the inset. The dashed vertical line marks the energy of two

non-interacting rotons at this temperature and pressure.

Fig. 1(a) shows the oscillatory optical birefringence in-

duced by the femtosecond laser pulse in the superﬂuid

at a temperature T= 1.38(2) K. The oscillations decay

exponentially with time, as reﬂected by the Lorentzian

line shape of their power spectrum shown in Fig. 1(b).

One can see that the spectrum is dominated by a sin-

gle excitation line, peaked at ω2r(T) = 17.01(1) K, which

corresponds closely to the energy of a roton pair found

in spontaneous Raman experiments [22, 23]. This value

is slightly lower than twice the energy of a single roton,

2∆(T), measured by means of neutron scattering at the

same values of temperature and saturated vapor pressure

[20, 30, 31], and marked by the vertical dashed line in the

inset to Fig. 1(b). The diﬀerence Eb= 2∆(T)−ω2r(T)

is the binding energy of the two-roton state, whereas

its decay rate is reﬂected by the measured linewidth

γ2r(T)=0.53(1) K.

Examination of the spectral proﬁle of the pump-

induced birefringence shows that the line shape is skewed

– a signature of a chirped damped harmonic oscillator

[32]. In comparison to a Lorentzian, the up-shifted low-

energy wing of the spectrum (“red-shading”) reﬂects a

FIG. 2. (a) Instantaneous frequency of the birefringence os-

cillations at T= 1.38(2) K as a function of time (thick red

line). See text for the calculation procedure. The dashed

blue line at the top marks the energy of two free rotons

2∆(T= 1.38 K). The thin black line reproduces the top

of the overall Lorentzian from Fig. 1(b). (b) Instantaneous

linewidth (left scale) and the corresponding decay constant

(right scale) of the birefringence oscillations at T= 1.38(2) K

as a function of time, obtained with a sliding 25 ps-wide win-

dow. Shaded regions in both panels represent the 95% conﬁ-

dence interval for the ﬁtted frequency and linewidth, respec-

tively. Black diamonds and circles, labeled with the corre-

sponding temperature in K, show the comparison to the ex-

isting theory of a two-roton decay (see text for details).

positive frequency chirp, i.e. an increasing instantaneous

frequency of the oscillator with time.

To quantify this, we ran a sliding time window across

the oscillatory signal [Fig. 1(a)], ﬁtting the windowed

part of the signal with an exponentially decaying sinu-

soid. The instantaneous frequency as a function of time

is plotted in Fig. 2(a). Here, the width of the sliding win-

dow was set at 25 ps, which provided an optimal trade-oﬀ

between the higher temporal resolution (narrower win-

dows) and lower uncertainties of the ﬁtting parameters

(broader windows). The analysis conﬁrms the upward

frequency chirp of the observed dynamics: the energy of

the two-roton state increases during the ﬁrst ≈50 ps of

its evolution, moving from the lower- to the higher-energy

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Ultrafastnon-equilibriumdynamicsofrotonsinsuperuidheliumA.A.Milner,1P.C.E.Stamp,1,2,3andV.Milner11DepartmentofPhysicsandAstronomy,UniversityofBritishColumbia,6224AgriculturalRd.,Vancouver,B.C.,CanadaV6T1Z12TheoreticalAstrophysics,Cahill,CaliforniaInstituteofTechnology,1200E.CaliforniaBoulevard,MC350...

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Ultrafast non-equilibrium dynamics of rotons in superuid helium A.A. Milner1P.C.E. Stamp1 2 3and V. Milner1 1Department of Physics and Astronomy University of British Columbia

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