Shapes and vorticities of superfluid helium nanodroplets

Gomez, Luis F.; Ferguson, Ken; Cryan, James; Bacellar, Camila; Tanyag, Rico Mayro P.; Jones, Curtis F.; Schorb, Sebastian; Anielski, Denis; Belkacem, A.; Bernando, Charles; Boll, Rebecca; Bozek, John D.; Carron, S.; Chen, Gang; Delmas, Tjark; Englert, Lars; Epp, Sascha W.; Erk, Benjamin; Foucar, L.; Hartmann, R.; Hexemer, Alexander; Huth, Martin; Kwok, Justin J.; Leone, Stephen R.; Heidkamp, Jonathan; Maia, Filipe R. N. C.; Malmerberg, Erik; Marchesini, Stefano; Neumark, Daniel M.; Poon, Billy K.; Prell, James S.; Rolles, Daniel; Rudek, Benedikt; Rudenko, Artem; Seifrid, Martin; Siefermann, Katrin R.; Sturm, Felix; Swiggers, Michele; Ullrich, J.; Weise, Fabian; Zwart, Petrus H.; Bostedt, Christoph; Geßner, Oliver; Vilesov, Andrey F.

doi:10.1126/science.1252395

Cited by 226 publications

(268 citation statements)

References 36 publications

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“…X-ray diffraction imaging of Xe doped He droplets revealed Bragg spots, confirming the existence of quantum vortex lattices that led to the condensation of 100-200 Xe clusters in a periodic array [18]. Positions and shapes of individual vortices could be deduced from diffraction images without Bragg spots by using a recently developed phase retrieval algorithm [19][20].…”

Section: Introductionmentioning

confidence: 94%

“…In addition, approximately 1% of the diffraction images exhibit streaks, i.e., pronounced intensity anomalies radiating away from the image center, see Fig. 1 (f-j) [18]. These images cannot be described by elliptical diffraction contours and exhibit very high aspect ratios of 1.5 < AR < 2.3.…”

Section: Introductionmentioning

confidence: 99%

“…Very recently we have shown that swiftly rotating 4 He droplets of sub-micrometer size may be produced from a cryogenic jet expansion into vacuum and that the droplet shapes can be studied via scattering of radiation from an x-ray free-electron laser (XFEL) [18]. X-ray diffraction imaging of Xe doped He droplets revealed Bragg spots, confirming the existence of quantum vortex lattices that led to the condensation of 100-200 Xe clusters in a periodic array [18].…”

Section: Introductionmentioning

confidence: 99%

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Shapes of rotating superfluid helium nanodroplets

et al. 2017

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Rotating superfluid He droplets of approximately 1 μm in diameter were obtained in a free nozzle beam expansion of liquid He in vacuum and were studied by single-shot coherent diffractive imaging using an x-ray free electron laser. The formation of strongly deformed droplets is evidenced by large anisotropies and intensity anomalies (streaks) in the obtained diffraction images. The analysis of the images shows that, in addition to previously described axially symmetric oblate shapes, some droplets exhibit prolate shapes. Forward modeling of the diffraction images indicates that the shapes of rotating superfluid droplets are very similar to their classical counterparts, giving direct access to the droplet angular momenta and angular velocities. The analyses of the radial intensity distribution and appearance statistics of the anisotropic images confirm the existence of oblate metastable superfluid droplets with large angular momenta beyond the classical bifurcation threshold.3

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shapes of rotating superfluid helium nanodroplets

et al. 2017

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“…It is immediate to generalize them to any trapping potentials and boundary conditions. They open a way to solve the long-standing problem of the BEC and other phase transitions [1][2][3][4][5][6][7][8][9][10][11][12], including a restricted canonical ensemble problem [2], and describe numerous modern laboratory and numerical experiments on the critical phenomena in BEC of the mesoscopic systems [22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Discussionmentioning

confidence: 99%

“…The problem of the critical region and mesoscopic effects is directly related to numerous modern experiments and numerical studies on the BEC of a trapped gas (including BEC on a chip), where N ∼ 10 2 − 10 7 , (see, for example, [22][23][24][25][26][27][28][29][30][31][32][33]) and superfluidity of 4 He in nanodroplets (N ∼ 10 8 − 10 11 ) [34] and porous glasses [35].…”

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confidence: 99%

Microscopic theory of a phase transition in a critical region: Bose–Einstein condensation in an interacting gas

Kocharovsky

2015

Physics Letters A

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We present a microscopic theory of the second order phase transition in an interacting Bose gas that allows one to describe formation of an ordered condensate phase from a disordered phase across an entire critical region continuously. We derive the exact fundamental equations for a condensate wave function and the Green's functions, which are valid both inside and outside the critical region. They are reduced to the usual Gross-Pitaevskii and Beliaev-Popov equations in a low-temperature limit outside the critical region. The theory is readily extendable to other phase transitions, in particular, in the physics of condensed matter and quantum fields.Published The problem of finding a microscopic theory of the second order phase transitions became one of the major problems in theoretical physics in 1950s after an invention of the powerful Green's functions and quantum field theory methods in the many-body physics. These methods include the Feynman's and Matsubara's diagram techniques, Wick's theorem, and Dyson's equation (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein). A major point is a failure of a Landau self-consistent field theory in a critical region, shown by the exact Onsager's solutions. However, all these standard methods turn out to be insufficient to solve the problem: The microscopic theory, which should connect the asymptotics of the ordered and disordered phases across the critical region, has not been found so far even for anyone of the numerous phase transitions.Here we present such a microscopic theory for a BoseEinstein condensation (BEC) in an interacting gas. We derive the fundamental equations for the order parameter and Green's functions, which are valid not only in the fully ordered, low-temperature phase, but also in the entire critical region and in the disordered phase. They resolve a fine structure of the system's statistics and thermodynamics near a critical λ-point. It becomes possible due to the newly developed methods of (a) the nonpolynomial averages and contraction superoperators [15,16], (b) the partial difference (recurrence) equations [17][18][19] (a discrete analog of the partial differential equations) for superoperators, and (c) a characteristic function and cumulant analysis for a joint distribution of the noncommutative observables. They allow us to take into account (I) the constraints in a many-body Hilbert space, which are the integrals of motion prescribed by a broken symmetry in virtue of a Noether's theorem, and constraintcutoff mechanism, responsible for the very existence of a phase transition and its nonanalytical features, [4,20,21] (II) an insufficiency of a grand-canonical-ensemble approximation, which is incorrect in the critical region [2,8] because of averaging over the systems with different numbers of particles, both below and above the critical point, i.e., over the condensed and noncondensed systems at the same time, that implies an error on the order of 100% for any critical function, (III) a necessity to solve the problem ...

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Chemistry and physics of dopants embedded in helium droplets

Albertini

Gruber

Zappa

et al. 2021

Mass Spectrometry Reviews

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Helium droplets represent a cold inert matrix, free of walls with outstanding properties to grow complexes and clusters at conditions that are perfect to simulate cold and dense regions of the interstellar medium. At sub-Kelvin temperatures, barrierless reactions triggered by radicals or ions have been observed and studied by optical spectroscopy and mass spectrometry. The present review summarizes developments of experimental techniques and methods and recent results they enabled.

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Shapes and vorticities of superfluid helium nanodroplets

Cited by 226 publications

References 36 publications

Shapes of rotating superfluid helium nanodroplets

Shapes of rotating superfluid helium nanodroplets

Microscopic theory of a phase transition in a critical region: Bose–Einstein condensation in an interacting gas

Chemistry and physics of dopants embedded in helium droplets

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