The Stark effect in superfluid 4 He with relative flows
A.S. Rybalko, S.P. Rubets, E.Ya. Rudavskii, R.V. Golovashchenko, S.I. Tarapov, V.N. Derkach, V.D. Khodusov, A.S. Naumovets, A.J. Nurmagambetov
TThe Stark effect in superfluid He with relative flows
A. S. Rybalko, ∗ S. P. Rubets, and E. Ya. Rudavskii
Verkin Institute for Low Temperature Physics and Engineering47 Nauki Av., Kharkov 61102 UA
R. V. Golovashchenko, S. I. Tarapov, and V. N. Derkach
Usikov Institute for Radiophysics and Electronics12 Ak. Proskury, Kharkov 61085 UA
V. D. Khodusov, A. S. Naumovets, and A. J. Nurmagambetov † Karazin Kharkov National University4 Svobody Sq., Kharkov 61022 UA (Dated: October 2, 2020) a r X i v : . [ c ond - m a t . o t h e r] O c t bstract We conducted series of experiments on observing a Stark-type effect in superfluid He in presence ofrelative laminar flows of the normal and superfluid components. It is designed a measurement cell whichallows us to simultaneously create hydrodynamic flows in the liquid and to carry out high-frequency radio-measurements at external electric field. We used a dielectric disk resonator that made possible to cover awide frequency range. In our experiments it was registered the spectrum of the dielectric disk resonatormodes, as well as narrow lines of absorption of a microwave radiation in He II on its background andin different conditions. We discovered that having in the liquid helium a relative motion of the normaland superfluid fractions in the temperature range of 1.4 ÷ ∼ − D, that in four order less of the characteristic dipolemoment of polar molecules. The comparison of our findings to values of the electric dipole moment (EDM)of elementary particles and nuclei is also performed. We sum up with brief discussion of extensions of theknown theoretical models and possible mechanisms of the EDM production.
Keywords:
Superfluidity, Stark effect, electric dipole moment, photons, rotons, recoil impulse.
PACS numbers: ∗ [email protected] † [email protected]; Also at Akhiezer Institute for Theoretical Physics of NSC KIPT, 1 Akademicheskaya St.,61108 Kharkov UA & Usikov Institute for Radiophysics and Electronics, 12 Ak. Proskury, Kharkov 61085 UA. . INTRODUCTION Symmetry plays a key role in physics. Invariance under continuous transformation groups un-derlies modern theories of elementary particle interactions; discrete transformations are involvedin fundamental and applied physics, from Cosmology to Spectroscopy of atoms and molecules.All physical processes, described in frameworks of standard (local) QFT, have to obey the promi-nent Schwinger-L¨uders-Pauli CPT-theorem. Before the Cronin-Fitch discovery of the CP-breakingin Strong Interactions, it was believed in deterministic (upon the evolution) nature of QFT. Cur-rently, breaking the time reversal in processes where the CP-invariance does not hold is commonlyadmitted.Breaking the CP-invariance is considered as one of the most viable scenario to explain theobserved mismatch between matter and anti-matter. The Standard Model and its extensions givevarious sources of the CP-violation; the electric dipole moment of quarks and leptons is amongthem. The latter came in the focus of our attention in view of unexpected finding the responseof the He Bose-Einstein condensate to an external source similar to the reaction of a mediumendowed with the electric dipole moment.Recall, the single atom liquid of He atoms with zero electric dipole moment in a free state ischaracterized by the absence of the solid state phase with approaching the absolute zero, revealsthe second order phase transition similar to that of magnetics and segnetics upon the critical tem-perature T = T λ , and possesses the superfluidity below the T λ [1]. Numerous experiments onbirefringence [2, 3], as well as on the temperature dependence of dielectric susceptibility (withinthe range of 1 ÷
10 kHz) [4–7], also confirm the absence of electric moments in the liquid. We cannotice it happened due to overlooking the dynamical properties of He II. However, experimentson revealing the influence of electric field on the superfluid liquid velocity in narrow slots [8] andon the transport over the superfluid film [9], as well as the Raman scattering of light [10], pointedout on possible manifestation of electrohydrodynamical properties at the seemingly electroneutralliquid. In the case of the light scattering, as specified by the superfluid theory and in accordancewith the fulfillment of the energy and momentum conservation laws, it was believed that the op-tical photon disappears and the Stokes photon is created. The difference between frequencies ofthe excited light and of the resulted Stokes’ photon is δf = 360 GHz, so that it corresponds to thethreshold energy (cid:52) = hδf ( h is the Planck constant) to create two quasiparticles – rotons – withthe opposite momenta [11]. 3he studies of [8–11] initiated new directions of investigations in electric properties of the HeII liquid. Starting from 2004 two series of experiments were performed on measuring the electricproperties of the liquid helium, which dramatically changed the view on the single-atom liquid ason a collection of interacting structureless spherical particles.The result of the first series of tests was consist in discovering the electric response (spon-taneous polarization) of He II upon the relative motion of normal and superfluid components inthe second sound wave and in the absence of an external electric field [12–20]. Herewith, it wasobserved the sharp difference in the laminar and turbulent flows (see [20]).To figure out the origin of the obtained response, we carried out the second series of testswith a dielectric disk resonator (DDR), embodied into the liquid helium [21–24]. We studied theinteraction of the liquid with whispering gallery modes of the DDR in the range, overlapping infrequency the rotonic part of the helium energy spectrum (100 ÷
200 GHz). It was shown that theabsorption spectrum of the optically transparent quantum liquid has the resonant peculiarities atthe frequency f rot = (cid:52) /h ; namely, a wide (several GHz) absorption resonance. As in before, (cid:52) is the energy gap corresponding to the creation of the roton quasiparticle. With approaching thetemperature to T λ the resonance width increased and a deformation occurred that made impossibleto extrapolate the resonance by the gaussian. The situation got changed with presence of artificiallycreated relative flows of the helium components around the resonator, when the flows coincide(or being opposite) in direction with the Poynting vector of the DDR whispering gallery wave[21–25]. In that case it is observed a narrow resonance in the background of a basement-typewide resonance, the location of which is almost independent on the temperature, and which, independence as on the pumping power as well as on the power of relative flows, undergo threestages: the absorption, the electromagnetic transparency, the induced radiation. It became clearthat the observed effect is caused by the difference between absorption and induced radiation [26]. A contradiction between theory and experiment consists in the fact that within the existent rotonmodels [27–29] it is impossible to explain as the process of the resonant absorption of EM wavesof the frequency 180 GHz [21], as well as the absorption of single photons of the roton frequency,generated by the embedded into He II and further excited dysprosium atoms [30].Since at the roton frequency the photon momentum is at many orders smaller than the rotonmomentum, the question arise: what is a mechanism to fullfil the momentum conservation lawin the abovementioned processes? And why the narrow resonance is turned out to be observableupon the relative motion of the normal and superfluid components? All of that required new strong4roofs and checks on the existence/absence of resonant photons exchange similar to that of inter-level transitions in atoms. We also posed a natural question on possible influence of an externalelectric field on the discovered the roton frequency narrow resonant line. Before, experimentalstudies of the Stark effect in helium were only conducted for the gas-state helium at high temper-atures in the frequency range, where the fine structure of the excited levels of the helium atombecomes manifest [26, 31–35]. The present study is aimed at verification of the efficiency of anexperimental device and at getting data on the impact of an external electric field on the resonantabsorption line of the EM waves in the superfluid helium.The paper is organized as follows. In section II we discuss the experimental methodic. Herewe recount the working parameters of our experimental setup and to overview the experimentalconditions. In Section III we recap the conditions under which the linear Stark effect in the liquidhelium is revealed. Section IV contains the analysis and discussion of the results. Here we inspectthe obtained result from different points of view, with trying to find the explanation of the Starkeffect within various theoretical models and approaches. We review in brief the existent contradic-tions between theory and experiment and propose new mechanism of the electric dipole momentgeneration, closely related to having the relative flows of the normal and superfluid components inHe II. We summing up the results and sketching up possible lines of the development in the lastsection.
II. HALLMARKS OF THE EXPERIMENTAL METHODIC
The measuring device, mounted in a cylindric chamber of the diameter 80 mm and of the length100 mm, consists of two parts: the system of radio measuring and the system of creating thehydrodynamic flows in the superfluid liquid (see Fig.1).In this experiment we followed the previously used methodic of [21–25]. The usage of dielec-tric disk resonators (DDRs) gets advantaged in compare, e.g., to cylindric ones by the following:a) measuring the absorption of EM waves on the family of whispering gallery modes (WGMs)with a high Q factor allows us to involve a large range of frequencies upon appearing the circularrelative flows of the normal and superfluid components; b) the artificially created relative motionof atoms compensates the Doppler shift upon exchanging among atoms the resonant photons ofthe roton energy (akin to the M ¨o ssbauer effect) and makes possible to observe a narrow line; c)during the WGM damping time the interaction path of a running EM wave with the hydrodynamic5uperfluid flow is equivalent to the column of the liquid of a few hundred meters of length. Noteto compare that in experiments on the Raman light scattering in the liquid helium the interactionpath of an EM wave of an optical frequency was ∼ . m.The disk dielectric resonator was made of the leuco sapphire; it has the diameter mm andthe width mm. The resonator was embedded into the liquid helium and served as the mainmeasuring element. The difference from the early used scheme consists in the following. To applya homogeneous radial electric field, it was made a hole of the diameter 3 mm in the center of theresonator 1 (see Fig.1), where a metal electrode 2 was inserted. The circular electrode 3 – of thecylindric shape – was installed coaxially to the resonator. It was made of a polyamide film of thewidth 30 mkm, the diameter 22 mm and of the height 0.91 mm. The resonator and the circularelectrode were supported by a frame; Fig.1 is not comprehensive in details. The thin conductinglayer of graphite powder with the BF glue, electrically connected with grounding, was appliedto the film surface. The value of constant electric field in the gap and its gradients was computednumerically. As follows from the numerics, the radial electric field in the gap between the cylindricsurface of the resonator and the ring electrode 3 is homogeneous within 10 percent along all thecylinder height. Since the capacitor formed by electrodes 2-3 has a complicated form and filledin part with the leuco sapphire, it is important to know the field value in the gap with the liquid.Its absolute value was calibrated in the following way: the conducting graphite film with the BFglue was put on the cylindrical resonator surface. The potential difference was applied in betweenthe electrodes 2 and 3, and it was measured the potential between surfaces of the resonator and theelectrode 3. After that the conducting layer has been washed away from the DDR surface.The SHF radiation was entered the cryostat working zone, while its exit was performed by useof two rectangular waveguides 4 from the nickel silver. A microwave radiation was connected tothe dielectric resonator (excitement and reception) by use of two pyramidal dielectric waveguides(antennas 5), located in the opposite directions on the disk plane. The ends of the antennas werecovered with an absorber. Under the radiation supply via the waveguide it was excited a whisperinggallery running wave, passing along the side surface (type HE m, ,δ ) of the resonator. The passingthrough the DDR signal was received by the reception antenna and registered by a semiconductordetector of the EM radiation, located at the opposite end of the nickel silver waveguide outside ofthe cryostat, i.e. at the room temperature (see [21] for more details).Specific experiments created at the vacuum conditions of the working chamber with the DDR Computations on the dc-field homogenety in the gap were performed by A. A. Girich. Ω ) on the 1mm distance from the resonator resulted in changing the resonant vibrationfrequency not more than 0.01% in the range of frequencies higher than 100 GHz. In particular,in the experiment at the frequency 62 GHz the frequency shift was 5 MHz, or 0.008%, and the Qfactor was fallen on 2% that did not significantly impact on the character of EM waves absorptionby the liquid. Upon the antennas location at the distance ∼ ÷ E dc of the applied voltage, as well as an alternating electric field E ac created by thewhispering gallery running wave. Both fields had the same radial direction from the center of theresonator and the condition E dc (cid:29) E ac has been satisfied.The hydrodynamic system of superfluid flows creation contained two Kapitza heat guns 6,which are thermally insulated flasks connected by nozzles to a helium bath (working chamber).There were thermometers of the resistance 7 and the heaters 8 inside the flasks. This allowedus to superheat the liquid helium in a controlled way to ∼ ∼ × mkm it was flowed out a laminar jet of the normalcomponent tangentially to the cylindric surface of the DDR. The normal component was slowingdown at the resonator wall and in the gap, but excited circular flows of the superfluid component.Thus, in the experiments, by turning the different guns on, it was possible to create the superfluidcomponent flows, the direction of which coincided or became opposite to the propagation directionof a whispering gallery wave. Forming a circular flow was accompanied with changing the topof the mode amplitude on 1 ÷ S/N ∼ , so that the multiple frequency pass with a stepof 8 kHz/0.1 sec allows us to observe the dynamics of appearing and narrowing the resonance line(registered curves 1,2,3,4,5 with the period of 3 sec). Hence, it becomes clear that the circularflow was restored during the time ∼
15 sec. Further scanning was carried out with the step of8 kHz/1 sec. The line became sharp. The large EM wave-liquid interaction path (300 ÷
500 m)together with the stability of the superfluid flows assist the narrow line detection. Unfortunately,we may only qualitatively observe the impact of the flows on the line, since studying the velocityfield around the resonator quantitatively does not seem possible.Within the experiments it has been registered the spectrum of the DDR modes and the narrowabsorption lines of microwave radiation in He II on its background. The measurements werecarried out at different power of the incoming radiation, at different directions and powers ofheat flows, at different values of the constant electric field. The main result of these experimentsconsists in the confirmation of: 1) existence of circular flows around the DDR; 2) existence ofthe narrow line of the resonant absorption at the frequency, corresponding to the roton minimalenergy ∆ for a leuco sapphire resonator with the step of the WGM ∼ ∼ III. SPLITTING THE ABSORPTION RESONANT LINE ON APPLYING A CONSTANT ELEC-TRIC FIELD
As it was mentioned before, to observe the narrow line it was needed to create a stationarysuperfluid flow in the gap. That is why at
T < T λ the procedure of the spectrum measurement waspreceded by switching the current through the located near the reception antenna gun heater on.Fig.3 includes preliminary results on observing the change of spectral characteristics of one of thewhispering gallery modes HE m, ,δ with the azimuthal index m = 128 , the frequency f ≈ GHzat the experimental conditions changing. This figure illustrates the change in the shape of theresonant curve of the mode as the temperature decreases from T λ to 1.4 K. At the temperature T = 1 . K (Fig.3a) the shape of the resonant curve does not have any peculiarities (the curve is8pproximated by the Lorentz (Peak shape) function) except that the ratio of “liquid–vacuum” stateamplitudes in the working chamber with the DDR ( A liquid /A vac ) becomes about 30% larger ofthe similar relation for the modes with azimuthal indices ∆ m = ± , that is in favor of a wideabsorption basement at the roton frequencies region. Note, that at T = 1 . K and at the normalconditions of the DDR’s environment applying the constant electric field up to 40 kV/m does notget a change in the resonant curve shape of this mode by its registration.Decreasing the temperature the mode location gets displaced in frequency due to changing thedensity of the liquid [36]; as a result, the mode and the narrow resonance absorption line mutuallycreep into each other. At the temperature T = 1 . K the locations of the mode maximum and ofthe narrow resonance coincide (Fig.3b). Fig.3b corresponds to the case of null external constantelectric field. In these conditions the resonant absorption frequency comes out as a dip (verynarrow line) on the amplitude-frequency characteristic of the mode. Moreover, the width of thenarrow line was influenced by heat flows created by Kapitsa’s guns. So, it could be possible toselect a power under which the width at the level of half of the amplitude was less than 40 ÷
50 kHz.Also it could be possible to initiate changing the regime of the resonant absorption to the inducedradiation regime by use of the superfluid component flows along the direction of the whisperinggallery wave propagation, similar to it was firstly demonstrated in [22].Below we will discuss on the narrow line in the absorption regime and on the influence on itthe electric field. The scanning was carried out with the step ∼ ÷ − W.On Fig.4 we present locations of frequencies for the left and the right resonances (the smallerand the larger in frequencies f − and f + ) in dependence on the value of the constant electric fieldrelatively to the narrow resonance frequency at the null field. As one can see, increasing theexternal field E dc the absorption frequencies change linearly with enlargement the field, and atlarge enough fields ( > kV/m) it is observed a deviation from the linear dependence towardslowering the frequencies. To clarify the nature of the observed results, we rearranged Figure 49s follows: we put the data of the bottom curve on the horizontal axis (field axis). Then, thetop curve data went the straight line in the whole range of frequencies. It became clear, thatwe experimentally observe the linear Stark effect. Unfortunately, we did not succeed with thesimultaneous measurement of the line locations for fields greater than 40 kV/m due to going thelines out the limits of resonant curve of the mode. IV. ANALYSIS AND DISCUSSION OF THE RESULTS
Previously, the experimental studies of the Stark effect have only been done for helium in thegas state at high temperatures [26, 31–35]. The experiments were performed at frequencies rangewhere the thin structure of the helium atom levels come out, on the Balmer series of lines (see,e.g., [32]). In that case, the Stark splitting of the excited states of the helium atom was studied. Inall of the mentioned papers it was observed a quadratic dependence of the lines displacement fromthe value of the electric field. The field values were reached 10 V/m.In our experiments the field strength values were in a few orders less in the liquid and at
T < K. If the quadratic Stark effect would be observed, the top curve on Fig.4 should be deflectedup of the linear one, while the bottom curve – to the down. In fact, as the external field increases,both lines of the Stark spectrum are displaced in frequency down. One may suppose that a one-sided deviation from the linear law corresponds to a polarization of the liquid by an external field.Then the model, satisfying the observable set of phenomena, looks as follows: the liquid heliumcontains the interacting to each other particles with a dipole moment, which being in a local field,form energy states in it. Owing to the Doppler dispersion of energy of the individual particlestates, a zone with the gap ∆ is created in the liquid. Below T λ the dipole interaction becomescoherent. Laminar relative flows of two parts of the liquid promote the observation of a thin lineof transitions. The lines split upon the action of a constant external electric field. In the alternate model of [24] it was pointed out that the roton is a collective excited mode of the helium as amany-particle system, hence one needs to take into account the change of state of the superfluid component inthe momentum conservation law. The superfluid component, as a third body, could take the needed surplus of themomentum to itself to fulfill the conservation law; moreover, like a macroscopic object, practically without takingthe energy away. This process is very like the same as that of the M ¨o ssbauer effect of transfering the momentum toa crystal as a whole. . Analysis based on the known models and facts Within the model on the test the data obtained were processed (according to recommendationsof [26], Chapter 5) by an empirical expression f ± = f rot ± dE dc h − αE dc h . (1)The first term on the r.h.s. of (1) is the absorption frequency f rot in the null field on account of acompensation of the Doppler shift in frequencies by a relative motion of interacting particles. Thisfrequency is related to the roton gap ∆ by the relation f rot = ∆ /h = dE loc /h . The second termof (1) describes the linear part of the Stark effect in the superfluid helium, and the third quadraticterm corresponds to the polarization part. Here h = 6 . · − J · sec is the Planck constant, E dc is the external field. The fitting parameters were the dipole moment of particles d , the local field E loc , the polarization coefficient α . The parameters d , E loc , α were determined by experimentaldata and are in SI units as: E loc = (6 . ± . · V/m, d = (2 . ± . · − C · m, α = 2 · − F · m . The local field turned out to be comparable with the Coulomb field at an electron orbit, thedipole moment came at four orders less than that of polar molecules, the polarization coefficientturned out to be comparable with the polarization of helium atoms.A classical estimation of the Coulomb field value for the helium atom nucleus in the 1s stateis about . ÷ · V/m. If a possible error in the determination of the field value in the gap,coming from a thermic contraction of the polyamide film, would be taken into account, the chargedisplacement in a dipole falls into the range of ÷ · − m (less than the classical electronradius). From microscopic point of view the present understanding on the description of the Heatom electron spectrum, being in a condensed matter of the same atoms, by use of 4 quantumnumbers does not allow one to interpret the observed structure of the absorption at the range of180 GHz. But, apparently, upon the absorption and radiation the same mechanism as in an isolatedatom takes place: upon transition from one state to another a system absorb or radiate the energyquanta.It is believed that electrons of the liquid helium at low temperatures are of 1s-state, and theapplied power of EM field ∼ − W of the 180 GHz frequency is not enough to excite morehigher in energy levels. It is also believed that the helium atom in the 1s-state does not have theenergy sublevels. However, the observed in the present work, as well as in [37], the linear Starkeffect makes evident the existence of a particle with the electric dipole moment, that stimulatescarrying out additional experiments on the sublevels existence or the presence of artifacts.11 . Extension of currect theoretical models
As we have noticed, the linear Stark effect in the liquid helium is highly likely explained byhaving the electric dipole moment in He II. Before turning to the discussion of possible mecha-nisms of its generation, recall that studies in the electric dipole moment of elementary particlesbecomes more and more popular in the context of different extensions of the elementary particlesStandard Model. For instance, the baryon-anti-baryon asymmetry of the visible Universe could berelated to the CP-breaking, which, in its turn, is directly related to carrying the electric dipole mo-ment by elementary particles. (See, e.g., [38–42] for reviews, and the results of the ACME group[43–45] in the measurements of the electron electric dipole moment (EDM) in atomic and molec-ular physics.) Note, however, the principle mismatch between the results of ours and that of theACME collaboration and theoretical computations based on QFT. The electron’s electric dipolemoment is theoretically predicted to be d e ∼ . × − ÷ − C · m (see [40] for recent com-putations of the e − EDM) and measured by the ACME collaboration to be | d e | < . · − C · m that (at least) 16 orders less that the electric dipole moment of the liquid helium. The valueof the helion ( He ++ ) light nuclei EDM is mostly determined by the neutron’s EDM [42], and isof the order d h ∼ . · − C · m. Therefore, the electric dipole moment of the liquid helium inpresence of relative flows can not be ultimately treated as that of its elementary constituents, suchas electrons, protons etc. (though we can not completely exclude such a possibility; see more onthis in the last section), and has rather a collective excitation nature.Various contemporary theoretical models of the liquid helium respond to a constant externalelectric field (see, e.g., [46–54]; this is presumably a non-comprehensive list) divide on two prin-cipal classes, in dependence on chosen consideration – macroscopic or microscopic. The morepreferable (more fundamental solution to the problem) microscopic point of view can not be suc-ceeded in full extent due to a fundamental drawback in the liquid helium theory: it should be atheory of a strong-coupling system [55, 56]. Moreover, within this picture the microscopic de-scription has also to be extended to the roton by itself, making the “What is a roton?” question[27–29, 46–48, 54, 55, 57, 58] to be of extreme importance.The following rationals give a doubt in the models of the roton as a localized/bound state ofatoms. Since the liquid helium is a quantum liquid, the laws of Quantum Mechanics have to befully applicable to the case. The dispersion | δ (cid:126)P | in the momenta for the roton’s localized statecan not be greater than the roton energy minimum ∆ . In fact, as it follows from the roton energy-12omentum relation (coming from the experimental E ( (cid:126)P ) curve), E = ∆ + (cid:16) δ (cid:126)P (cid:17) µ (2)in the proper reference frame. ∆ (cid:29) (cid:16) δ (cid:126)P (cid:17) / µ , that, together with ∆ (cid:29) k B T , results in δP ∼ (2 µk B T ) / . (Here µ ∼ . m He .) Then, the Heisenberg uncertainty relation at T ∼ . K leadsto δx ∼ (cid:126) δP ∼ . · − m , (3)so that the dispersion in the coordinate becomes about twice larger than the natural interatomicdistance in He II [59]. The roton, as a collection of quantum particles, becomes hard to localize(a non-dynamical, i.e., a topological and still uncovered conservation law is required to this end),and we conclude, as in before, that it is rather a collective excitation mode for the quantum liquidas a whole.Before turning to the macroscopic consideration let us make a brief conclusion on the micro-scopic atomic structure of He II in the superfluid phase. The analysis of the experimental datahas resulted in fixing the parameters of (1); the intensity of external field is of ∼ V/m (seeFig.4). It is easy to see that the linear part of (1) is about . · − in h − · sec − . The quadraticin the field part of (1) becomes − in the same units. Certainly, the linear part contributes thevalue of two orders higher than the quadratic part, resulting in the linear Stark effect. However,the linear Stark effect in atomic physics is rather an exclusion than a rule [32, 60, 61]. In the caseof the helium atoms [35, 62] it means that the most contribution follows from s s ≡ s electronorbital configuration preferably than from s s (or higher states like s p etc.). In other words,the wave function of He atoms in the liquid state is mostly the product of two hydrogen-typeground state wave function: one of the doubled charge Z = 2 , and the other one of the charge Z = 1 . Hence, commonly one of the two helium electrons is located far enough of the atomiccore, making possible the polarization by a weak external field.Now we turn to phenomenology. The main advantage of the macroscopic description (cf. forinstance [27, 55, 56]) consists in the transition to the dual description of the quantum liquid at thestrong-coupling regime in terms of weakly-interacting quasi-particles – phonons and rotons (lasttime maxons were separated to additional class of quasi-particles). Therefore, the microscopicstructure of the quantum liquid constituents becomes not so important, so that the description isbased on average characteristics of the liquid. 13ne of the characteristics of He II is the frequency corresponding to the roton minimum, f rot ∼
180 GHz, entering the empirical expression (1) in before. Manifestation of this quantityin many experiments on the electrical activity of the liquid helium (see, e.g., [12, 13, 19, 21–23])sets possible to conclude that this quantity is the internal resonant frequency of the medium and isthat of fundamental importance.Within the quasi-particles formalism the narrow dip near the resonant frequency of He II ina weak external electric field can be treated as a corollary of dynamical processes of absorp-tion/radiation of a super-high frequency wave by the medium, or, more precisely, of QuantumElectrodynamics of rotons. For instance, the analysis of the energy and momentum conservationlaws for the Raman scattering of the light [53] results in a narrow domain of physically admissiblefrequencies (of the kHz order, cf. Fig.3) and of wave vectors of the EM radiation near the rotonminimum. It is worth mentioning the admissible narrow domain in the wave vectors of radiationincludes momenta near the roton minimum which are opposite in the direction (resulted in Fig. 3cor Fig. 3d). It corresponds, by the momentum conservation law, to 2 → the momenta of which are of the same order, but opposite in the direction –the so-called R + and R − rotons [27], in accordance to the orientation of their group velocity withrespect to the direction of the heat flow (towards or against).Since the electric respond of the liquid directly depends on having the heat flows, to which R + / R − rotons inherent, the induced electric dipole moment has naturally to be dependent on maincharacteristics of the flow – velocity and/or acceleration – and includes f rot as a fundamentalcharacteristic of the quantum liquid respond. On account of these observation the dimensionalityarguments suggest the following expression for the induced electric dipole moment: (cid:126)d = e (cid:126) ∆ (cid:126)v g = e (cid:126) ∆ (cid:18) P − P µ (cid:19) (cid:126)PP , (4)with the roton’s group velocity (cid:126)v g . As a result, standard computations of the average value of (cid:126)d with the equilibrium distribution function of the rotons (details of which we will postpone forpublishing elsewhere) and with the known values of He II parameters (see, e.g., [59]), lead to thefollowing value of ¯ d ≡ | (cid:126)d | at T ∼ . K: ¯ d ≈ . · − C · m , (5)which is close to the experimentally observed value (2 . ± . · − C · m. The photon’s C -parity excludes processes with a single photon, while kinematical arguments prohibit the appear-ance of a single roton in the Raman scattering. Note that the right order of the induced electric dipole moment has been recovered from other phenomenological . SUMMARY AND CONCLUSIONS We have demonstrated the device that makes possible to excite the circular superfluid flowsalong a running wave of the whispering gallery of the dielectric disk resonator and to carry out theelectromagnetic spectroscopy of He II. It has been revealed that at the laminar relative flows of thenormal and of the superfluid components it is observed the narrow line of the EM spectrum at theroton frequency (180 GHz), which splits by a constant electric field.The observed linear Stark effect is directly related to the induced electric dipole moment (EDM)of the liquid helium. However, our arguments support the view of the electric dipole moment as areaction of the entire medium to a given action of a weak external field, rather than a contributionof its separate microscopic constituents to the effect. One of the facts making evident this point ofview is given by comparing the obtained value of the liquid helium EDM to the electron’s electricdipole moment: the value of the latter, measured by the ACME group, is in 16 orders less thatthe former. Possible EDM values of the helion – the doubly ionized He atom – are of 13 ordersless than that of the liquid helium. In theory, the value of particle density in the liquid helium islarge enough to fill this huge gap. However, the specific realization of a mechanism leading toexact matching the average value of the total electric dipole moment of the He II constituents tothat of our findings definitely deserves additional studies. Hence, at the present state of the art, weconclude that correct microscopic arguments, based on the internal (atomic-electron) structure ofthe considered Bose-Einstein Condensate (BEC), are either still missing to reproduce the precisevalue of the He II EDM, or can not be applied in full extent due to the strong-coupling nature ofthe liquid. At the same time the consideration of the collective behavior of the BEC as a whole(in terms of quasi-particles) is quite reasonable and is one of the ways to describe different non-apparent properties of the liquid helium.Surely, a lot of work should be done before achieving the ultimate explanation of the observedphenomena discussed here. From the point of view of theory, the proposed by us expression forthe EDM (formula (4)) has to be refined for a non-trivial geometry of the experiment (such as[13]); from the experimental point of view it would be interesting to find frequencies of the liquidrespond corresponding other (than the Raman scattering) admissible processes of interacting EMwaves with collective excitations of He II. We are planning to turn to these and other related tasks rationales in [50]. However, in contrast to the approach of [50], where at least two arbitrary fitting parameters wereused, the proposed expression of the induced electric dipole moment (4) contains solely the proper characteristicsof the liquid helium.
15n the future.We conclude with noting the following important detail. Specifically, the EDM of He II isthat of its collective excitation modes – quasi-particles. It was pointed out long before [63] thecollective excitations can also be supplied with different quantum numbers, usually inherent toelementary particles. One may assign to quasi-particles an angular momentum, analog of spin,endow them with the parity quantum number and so on. Our findings extend this list to the electricdipole moment, which now can be associated to rotons. So we can observe, again and again, amystical intertwining between Elementary Particle and Condensed Matter Physics.
ACKNOWLEDGEMENTS
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E < kV/sm are borrowed from [36]. The error bars point the error values in the determination of absolutevalues of the electric field in the gap and of the 180GHz frequency.kV/sm are borrowed from [36]. The error bars point the error values in the determination of absolutevalues of the electric field in the gap and of the 180GHz frequency.