Controlled Excitation of Rotons in Superfluid Helium with an Optical Centrifuge We experimentally demonstrate a controlled transfer of angular momentum to roton pairs in superfluid
helium. The control is executed with an optical centrifuge and detected with coherent time- and frequencyresolved Raman scattering. We show that the sign of the Raman shift, and hence the orientation of the
angular momentum transferred from the laser field to the rotons, is dictated by the centrifuge. The
magnitude of the shift reflects the two-roton energy and indicates that the centrifuge-induced roton pairs are
far from the equilibrium with the quantum bath. The observed decay of the coherent Raman signal suggests
that the decoherence is governed by the scattering on thermal rotons and phonons. The demonstrated
method offers ways of examining microscopic origins of superfluidity by controlling collective excitations
in superfluids.Superfluid helium is one of the paradigm systems for
studying collective excitations in strongly interacting
many-body quantum systems. As first proposed by
Landau [1,2], elementary excitations in superfluid 4He
(He II) consist of phonons, maxons, and rotons. Many
aspects of superfluidity can be described and explained by
the dispersion properties of these quasiparticles and their
interactions. Until recently, they have been studied predominantly with experimental tools sensitive to the equilibrium steady-state dynamics of the superfluid—neutron
scattering [3,4] and spontaneous Raman scattering [5,6]
(for a recent review, see Ref. [7]). The latter approach
followed a theoretical prediction that rotons can be optically observed only in pairs, owing to the big momentum
mismatch with a much smaller momentum of a photon [8].
Spectral broadening of the single-roton peak in experiments with neutrons [9–11], and the two-roton peak in
Raman scattering[6,12] has been associated withroton-roton
and roton-phonon collisions in the gas of quasiparticles in
thermal equilibrium [13–16]. Recently implemented timeresolved optical study of roton pairs revealed rich nonequilibrium dynamics with both the central frequency and
spectral width of the two-roton peak changing on a picosecond timescale during the thermalization of rotons with
the superfluid bath [17].
In addition to the energy shift and linewidth of scattered
light, its polarization provides further insight into the nature
of collective excitations in superfluid helium [18]. Since
rotons are bosons, the angular momentum l of a roton pair
can attain only even values [16]. Polarization analysis of the
two-roton Raman spectra of He II showed that the scattering is predominantly of d-wave character, which stems
from the “dipole–induced-dipole” interaction mechanism
[19]: The incident light polarizes helium atoms, whose
fluctuating density (governed by phonons and rotons)
results in an electric field at the neighboring volume of
other He atoms; the induced oscillating polarization of the
latter is responsible for the emission of the scattered light.
Experimentally observed d-wave scattering of light by a
roton pair implied an exchange of two units of angular
momentum [19,20].
Whereas spontaneous Raman scattering samples thermal
roton pairs with isotropically distributed vectors of angular
momentum l, we utilize stimulated Raman scattering to
excite two-roton states in a controlled way with a welldefined orientation of l. To that end, we employ an optical
centrifuge—a unique laser tool previously used for the
controlled rotational excitations of molecules [21–24], to
control the transfer of angular momentum from the laser
field to the collective excitations in a superfluid.
We detect the rotational state of a roton pair by means of
coherent Raman scattering (CRS) of weak probe laser
pulses. Owing to its polarization sensitivity [24,25], CRS
probing not only indicates that the centrifuge-induced
two-roton excitation carries two units of angular momentum (as inferred from earlier experiments), but also shows
that its orientation is dictated by the direction of rotation of
the optical centrifuge. Femtosecond time resolution of the
coherent Raman technique enables us to study the decay of
the laser-induced two-roton angular momentum and compare it to the lifetime of the roton pair.
The experimental setup is illustrated in Fig. 1.
Femtosecond pulses from a Ti:sapphire laser system
(35 fs pulse length, 1 KHz repetition rate, 793 nm central
wavelength) are shaped into the field of an optical centrifuge—a laser pulse whose linear polarization rotates with
accelerating rate [21]. Our setup for producing the centrifuge has been described in a recent review [26]. Briefly,
we split the spectrum of each pulse in two equal parts
using the original recipe of Villeneuve et al. [22]. The twospectral parts are then frequency chirped in opposite
directions and circularly polarized with an opposite handedness. When combined together, interference of such laser
fields results in the rotation of the polarization vector with
an angular frequency growing linearly in time at the
constant rate of ≈100 GHz=ps. As will be shown below,
a ≈4 ps-long centrifuge pulse, used in this work, sweeps
through the energy of a two-roton state (≈360 GHz) and
leads to its efficient excitation.
The centrifuge pulses (≲40 μJ pulse energy, ≲1.5 ×
1012 W=cm2 peak intensity) are focused in the bulk liquid
helium, condensed in a custom-built optical cryostat. By
pumping the helium gas from the cryostat, the temperature
of the liquid can be varied between 1.4 and 4.2 K at the
respective saturated vapor pressure (SVP) above the
liquid’s surface. Each centrifuge pulse is followed by a
weak probe pulse, derived from the same laser system and
spectrally narrowed down to the bandwidth of ≈100 GHz
(pulse length of 4.4 ps) in a standard 4f Fourier pulse
shaper [27]. Frequency doubling of probe pulses shifts their
central wavelength to 398 nm, which allows an easy
separation from the centrifuge beam with a spectral filter.
Probe pulses are circularly polarized at the entrance to
the cryostat by a circular polarizer (a combination of a
linear polarizer and a quarter-wave plate, CPþ in Fig. 1),
and passed through a circular analyzer of an opposite
handedness (CP−) after exiting the sample. This choice of
an input or output probe polarization stems from the
conservation of angular momentum in a parametric fourwave mixing process of Raman scattering, in which one
circularly polarized photon from the centrifuge field is
absorbed, while another photon of opposite circular polarization is returned back into the centrifuge field via
stimulated emission. As a result, two units of angular
momentum are exchanged between the laser field and the
medium, while coherence is induced between the participating angular momentum states. Owing to the latter, the
polarization handedness of the scattered light is opposite to
the input probe polarization [24]. The probe spectrum is
recorded with a 100 GHz (4.8 K)-resolution spectrometer
as a function of the centrifuge-probe delay time, the
temperature of the liquid, and the direction of the centrifuge
rotation.
Figure 2(a) shows a set of probe spectra taken at the
constant liquid helium temperature of 1.37  0.02 K and
different delays between the centrifuge and probe pulses.
The two-roton Raman peak appears when the probe pulse is
scanned in time across the 4 ps-long centrifuge, and decays
thereafter. We define zero delay (Δt ¼ 0) as the time atwhich the Raman signal at the two-roton frequency reaches
its maximum. Strong nonresonant Raman background,
owing to the instantaneous electronic response of the liquid
to the excitation fields, dictates the minimum delay of
≳4 ps. Here, we started the scan at Δt ¼ 10 ps and
normalized the recorded spectra to the highest peak at
the shortest delay. All spectra show a clear Raman line
shifted from the central probe wavelength by 17  1 K,
which agrees well with the energy of a two-roton state at
this temperature [5,8]. The accuracy of the energy shift and
the measured line width are both limited by the resolution
of our spectrometer. To within the sensitivity of our
detection, no theoretically expected four-roton peak [28]
is visible around 35 K. The first attempt to detect four-roton
excitations in He II has been reported by Udagawa et al.,
who observed a clear maximum at the four-roton energy in
their spontaneous Raman spectra [19]. However, its interpretation as the four-roton resonance remained inconclusive due to the disagreement with the predicted pressure
dependence. The authors suggested that other excitations
(e.g., at twice the maxon energy) may have obscured the
weak four-roton signal. Together with those earlier findings, the absence of the four-roton peak in our data calls for
further experimental and theoretical investigation.
Increasing the delay from 10 to 54 ps results in the
exponential drop in the peak amplitude. This is presented in
panel (b) of Fig. 2. The amplitude of each Raman line was
calculated by fitting it to a Gaussian profile. The decay of
the Raman signal is well described by an exponent with a
time constant of 11.2  1.7 ps [solid red line in Fig. 2(b)].
This time is noticeably shorter than a two-roton equilibrium
lifetime of ≈36 ps at T ¼ 1.37 K, obtained from both the
neutron scattering [29] and the spontaneous Raman data
[12]. It indicates the underlying nonequilibrium dynamics,
similar to that found in our recent work on roton pairs
excited with a linearly polarized femtosecond pulse [17].
There, the two-roton energy increased from 16.90 to
17.05 K in the same time window between 10 and 50 ps
(not visible in the Raman shifts in Fig. 2 due to the limited
spectral resolution). Since roton energy increases with
decreasing temperature of the superfluid [16,30], it was
attributed to the ultrafast cooling of initially hot roton pairs
by the colder bath (hereafter, by “hot” we mean in a local
environment, whose temperature is higher than the surrounding bath). Noteworthy is the very similar time
constant of 11.6  0.5 ps for the energy relaxation found
in that study and the CRS amplitude decay observed here.
It suggests that the decoherence of the roton pair’s angular
momentum is governed by the same mechanism as its
equilibration with the quantum environment.
From the fit to the exponential decay in Fig. 2(b), we find
that the amplitude of the Raman signal approaches a
nonzero asymptotic value of ð3.4  2.1Þ% relative to its
extrapolated strength at Δt ¼ 0. We attribute this result to
the temperature dependent decay constant, which becomes
longer as the centrifuge-excited roton pairs cool down.
The effect appears similar to an almost twofold decrease of
the roton linewidth observed on the same timescale in our
previous work [17].
The dependence of the Raman spectra on the temperature of helium at a fixed delay of 6 ps is shown in Fig. 3(a).
The broad temperature-independent peak around 30 K
corresponds to the nonresonant Raman background, which
stems from the instantaneous electronic response of theliquid to the probe and centrifuge pulses, partially overlapping in time due to a rather short probe delay. The effect
is similar to the nonresonant background in the Raman
spectra of centrifuged molecules [24]. The location of the
peak is determined by the centrifuge frequency at the end of
the centrifuge pulse, and is not related to the excitation of
rotons.
The spectra were normalized to the highest peak, corresponding to the lowest temperature of 1.37  0.02 K. As we
increased the temperature of the liquid to 2.15  0.02 K, the
two-roton Raman line weakened and shifted to lower
energies. The decrease of the amplitude of the Raman peaks
is plotted in panel (b) of Fig. 3, where it is fitted to an
exponential dependence ∝ exp ½−T=T0 with T0 ¼ 0.25 
0.04 K (solid red line). Towithin the accuracy of our method,
the coherent Raman signal reaches zero at the lambda point.
This result is consistent with the two-fluid model, according
to which the roton excitations disappear at Tλ together with
the superfluid component [7,10,32]. Unfortunately, taking
data at T > Tλ proved impossible due to the sharp drop in
thermal conductivity of liquid helium above the phase
transition. The latter caused thermal instabilities in the liquid
at the focus of the laser beams, accompanied by large
fluctuations in refractive index, disrupting the spatial coherence and preventing the formation of coherent Raman signal.
The influence of the He II temperature on the Raman
shift, and hence on the energy of the roton pairs excited by
the optical centrifuge, is shown in Fig. 3(c). Comparing our
data with the results of the neutron scattering experiments
[29,31] (solid red and dashed blue lines, respectively), we
again notice the signs of nonequilibrium dynamics. Lower
than expected (for a given temperature of He II) energy of a
roton pair indicates that its local environment is substantially hotter than the surrounding medium, suggesting that
the rotons did not have enough time to equilibrate with the
bath. The observed two-roton energy is lower than in Fig. 2,
owing to the shorter centrifuge-probe delay and correspondingly farther-from-equilibrium state of roton pairs.
Our ability to control the two-roton excitations with the
optical centrifuge is illustrated in Fig. 4. Here, the two
coherent Raman spectra were recorded under identical
conditions, except from the direction of rotation of the
centrifuge field, indicated near the respective Raman peak.
The Stokes peak, down-shifted from the central frequency
of the probe pulse by the two-roton frequency (blue line), is
observed when the polarization vector of the centrifuge is
rotating in the same direction as the circular polarization of
the probe. Changing the direction of the centrifuge rotation
to the opposite results in the appearance of the anti-Stokes
peak (red line).
The observed effect of rotational directionality on
coherent Raman scattering is very similar to what has
been seen in numerous experiments on centrifuged molecules (for a recent review, see Ref. [26]). At any given
time, the centrifuge pulse supplies two photons of opposite
circular polarization, one shifted above and one below its
central frequency. An absorption of the higher-energy
photon, together with a stimulated emission of the lowerenergy one, results in the transfer of two units of angular
momentum to the centrifuged system. In the experiments
with centrifuged molecules, repeating this process N times
makes the molecule climb the rotational ladder of states
higher and higher in multiple steps of 2ℏ. At the end, the
molecular angular momentum increases by ΔJ ¼ 2ℏN,
while its direction is determined by the handedness of the
centrifuge field.
In the case studied here, the predominant d-wave scattering of light from a two-roton state found in the earlier
experiments on spontaneous Raman, suggests that the
interaction between the optical centrifuge and the superfluid
helium should terminate at the very first Raman step with
Δl ¼ 2ℏ. This would result in a single Raman line, in
agreement with what we observe and in contrast to the
comb of multiple rotational Raman lines typical for a freerotating molecular systems [24]. Yet similarly to the molecular case, the handedness of the centrifuge field is transferred
to the two-roton state and is carried by that collective
excitation for more than 50 ps, long after the centrifuge
pulse is gone.
In summary, we experimentally demonstrate a controlled
transfer of angular momentum from the laser field to
two-roton excitation in superfluid helium. The transfer is
executed with an optical centrifuge and monitored with
coherent Raman scattering. We show that roton pairs
excited by the centrifuge retain information about the
direction of the centrifuge rotation for ≳50 ps, at least
an order of magnitude longer than the centrifuge pulseThe decoherence rate of the induced angular momentum,
determined through the decay of coherent Raman signal, is
very similar to the recently found rate at which laser-excited
hot rotons equilibrate with the colder environment [17].
Thus, both processes can be associated with inelastic
collisions of the centrifuged roton pairs with thermal rotons
and phonons.
The combination of time and frequency resolution offered
by the CRS technique allowed us to measure the two-roton
energy at short delays after the excitation pulse, down to 4 ps,
much shorter than in our previous time-resolved study, where
a scan of at least 20 ps had to be carried out for determining an
average roton energy in that broad time window. Our results
suggest that shortly after the laser pulse, the excited roton
pairs may be much further from the equilibrium than what
can be inferred from a single exponent fitted at later times.
The observed shifts of roton energy at short delays indicate
their effective temperature comparable with (and possibly
even higher than) Tλ, almost a full degree above the
temperature of the superfluid bath.
Applying an optical centrifuge to inject angular momentum in He II, and using coherent optical methods to track
the centrifuge-induced collective excitations, offers a way
of studying them in strongly interacting quantum systems
far from equilibrium. Improving the spectral resolution of
our detection scheme, which is currently under way, will
enable us to reveal further details of these nonequilibrium
coherent dynamics of rotons in superfluid helium.
This research was supported by the Natural Sciences and
Engineering Research Council of Canada (NSERC).