Seminars

Vortices in liquid He, energy spectrum of quantum turbulence, quantum turbulence in atomic BECs

Following last week’s seminar, I will talk about quantum hydrodynamics and turbulence [1]. I will discuss important issues
by referring to both superfluid helium and atomic BECs.

• 1.Visualization of quantized vortices in superfluid 4He: A major recent development in the field of superfluid helium has been brought about by visualization experiments. The group led by Lathrop succeeded in visualizing quantized vortices using solid hydrogen particles [2], and subsequently in observing their reconnections. Minowa et al. employed silicon particles generated by laser ablation to achieve the direct excitation of Kelvin waves and to observe their three-dimensional helical structure [3]. Furthermore, through measurements of the chirality and propagation direction of Kelvin waves, they succeeded for the first time in identifying the orientation of vorticity in quantized vortices.

• Energy spectrum of quantum turbulence Turbulence is not merely a disordered arrangement of vortices; rather, the confirmation of statistical laws such as the Kolmogorov law provides crucial evidence. The energy spectrum of quantum turbulence (QT) within the Gross–Pitaevskii (GP) equation framework was first investigated by Brachet and collaborators. As in the case of atomic BECs, the GP equation
  describes a compressible fluid, and thus the energy spectrum must be decomposed into an incompressible component due to quantized vortices and a compressible component due to phonons. Starting from a Taylor–Green vortex, they studied decaying QT and demonstrated
  that the incompressible spectrum exhibits a −5/3 scaling during the decay process [4]. Subsequently, Kobayashi and Tsubota introduced large-scale forcing and small-scale dissipation into the GP equation to generate steady-state QT, and confirmed that the incompressible spectrum follows the −5/3 law in this regime [5].

• . Quantum turbulence in atomic BECs Because an atomic BEC is a finite system confined by a trapping potential, QT cannot be generated simply by driving flow as in superfluid 4He. Instead, several methods have been proposed to create QT, including manipulations of the trapping potential. Kobayashi and Tsubota demonstrated that biaxial rotation of a BEC can induce turbulence [6], and, building on this idea, Bagnato et al. succeeded in realizing and observing three-dimensional QT through controlled modifications of the trapping potential [7]. Two-dimensional QT has also been realized [8]. However, these remain finite trapped systems with only a limited number of vortices. For turbulence, the verification of statistical laws is desirable, but such observations were hampered by the nonuniform density of the trapped gas. Recently, however, Navon et al. created turbulence in a BEC confined by a box potential, succeeded in demonstrating a power-law density spectrum [9], and observed a cascade of excitations flowing from low to high wave numbers [10].

[1] M. Tsubota, K. Kasamatsu, Quantum Hydrodynamics and Turbulence (Oxford Univ. Press) (2025).
[2] G. P. Bewley et al. Nature 441, 588(2006).
[3] Y. Minowa, Y. Yasui, T. Nakagawa, S. Inui, MT, M. Ashida, Nat. Phys. 233, 21(2025).
[4] C. Nore, M. Abid, and M. E. Brachet, Phys. Rev. Lett. 78,3896 (1997); Phys. Fluids 9, 2644 (1997).
[5] M. Kobayashi, MT, Phys. Rev. Lett. 94, 065302(2005); J. Phys. Soc. Jpn. 74, 3248(2005).
[6] M. Kobayashi, MT, Phys. Rev. A76, 045603(2007).
[7] E. A. L. Henn et al. , Phys. Rev. Lett. 103, 045301 (2009).
[8] K. E. Wilson et al., Annu. Rev. Cold At. Mol. 1, 261 (2013) : W. J. Kwon et al., Phys. Rev. A 90, 063627 (2014).
[9] N. Navon, A. L. Gaunt, R. P. Smith, Z. Hadzibabic, Nature 539, 72 (2016)
[10] N. Navon, C. Eigen, J. Zhang, R. Lopes, A. L. Gaunt, K. Fujimoto, MT, R. P. Smith, Z. Hadzibabic, Science 366, 382 (2019)

Classical turbulence, quantum hydrodynamics, vortex lattices in rotating Bose-Einstein condensates (BECs)

Quantum hydrodynamics and turbulence [1] have long been studied in superfluid helium since the 1950s, as well as in atomic Bose-Einstein condensates (BECs) since 1995. In this two-part seminar series, I will present this topic in an accessible way.

1. Classical turbulence: Turbulence is an important problem in both fundamental science and engineering [2,3]. It is a strongly nonlinear and non-equilibrium phenomenon, and therefore very challenging. About 500 years ago, Da Vinci sketched Fig. 1, illustrating the Richardson cascade, in which large vortices break down into smaller ones. However, vortices in classical viscous fluids are unstable and not uniquely defined, so confirming this picture is not straightforward. Another important perspective on turbulence is its statistical laws. The most important statistical law of fully developed turbulence is Kolmogorov’s −5/3 law of the energy spectrum, which has been confirmed by many experiments and numerical simulations.

2. Quantum hydrodynamics: In parallel with such studies in fluid dynamics, research on the superfluidity of liquid helium has progressed in the field of low-temperature physics. This system is characterized by the Bose–Einstein condensation of 4He atoms. Many of its distinctive
   phenomena are explained by the two-fluid model, which describes the system as consisting of an inviscid superfluid and a viscous normal fluid, with their relative fractions determined by temperature. Moreover, vortices in the superfluid become quantized vortices with discrete circulation, which have become a defining hallmark of the quantum hydrodynamics of this system.
   Turbulence generated by such quantized vortices is referred to as quantum turbulence. The typical platforms for quantum hydrodynamics are superfluid helium and atomic BECs. In the strongly correlated Bose system of superfluid ⁴He, the vortex filament model is employed. In contrast, for atomic BECs, the Gross–Pitaevskii (GP) equation provides a quantitatively accurate description.

3. Formation of a lattice of quantized vortices in rotating BECs One of the central problems in quantum hydrodynamics is the formation of a quantized vortex lattice in a rotating BEC. In the case of a classical viscous fluid, when the container is rotated, the fluid undergoes rigid-body rotation with the same rotation frequency as the container. However, due to the quantization of circulation, a quantum fluid does not behave in this way. Instead, a number of quantized vortices proportional to the rotation frequency penetrate into the condensate, forming a triangular lattice, thereby realizing rigid-body rotation of the superfluid. This phenomenon had already been known in superfluid helium, but the dynamics leading to it were observed by the experimental group at ENS [4]. A BEC confined in a harmonic trapping potential first
   undergoes quadrupole oscillations, after which its surface becomes unstable, allowing quantized vortices to enter. Ultimately, a triangular lattice is formed. Such behavior has been confirmed by numerical simulations of the GP equation [5].

[1] M. Tsubota, K. Kasamatsu, Quantum Hydrodynamics and Turbulence (Oxford Univ. Press) 2025.
[2] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press) 1995.
[3] P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press) 2015.
[4] K. W. Madison et al., Phys. Rev. Lett. 86, 4443 (2001).
[5] MT, K. Kasamatsu, M. Ueda, Phys. Rev. A65, 23603(2002): K. Kasamatsu, MT, M. Ueda, Phys. Rev. A67,33610(2003)

Title of seminar: Quantum Fluctuation Forces Near Material Interfaces

Abstract:

Fluctuations are ubiquitous in classical and quantum physics, affecting various disciplines like biophysics, gravity, chemistry, and cosmology. In recent years, the pursuit of miniaturization has led to a surge in interest in electromagnetic quantum fluctuation-induced interactions, both for fundamental and technological reasons. Despite often being imperceptible at the macroscopic scale, these interactions can indeed be rather significant in microscopic systems, presenting challenges as well as opportunities for quantum technologies. Paradigmatic examples include van der Waals and Casimir forces, which can be beneficial or disruptive in device design. Recent advancements have enabled exploration of nonequilibrium physics, quantum electrodynamics, atomic, and condensed matter physics as well as their interfacing within this research domain. Understanding these forces provides novel perspectives on the underlying physics and paves the way for future developments.

Title of seminar: Towards the First Measurement of Parity Violation in Chiral Molecules – New Attempts and Future Prospective

Abstract:

A fundamental discovery of this century is that our Universe is “left” handed (Weinberg-Salam-Glashow theory), the electro-weak interaction (parity-odd) gives rise to primarily left-spinning electrons during beta decay. In 1957 Lee and Yang discovered parity violation (PV) in the K+ decay, which was confirmed shortly after by Wu et al. for the b-decay. In the last decade PV effects in atomic transitions have been measured and calculated to high accuracy confirming the so-called standard model in particle physics. PV through Z-boson exchange between electrons and nucleons, leads to a small energy difference between enantiomers of chiral molecules although there is no experimental verification yet
of this distinct symmetry breaking effect despite many attempts. Current high resolution optical spectroscopy carried out in the CO2 laser frequency range (878-1108 cm-1) at LPL in Paris achieves resolutions of about 1 Hz. Recent calculations in our group applying the standard model show that PV effects in vibrational transitions of chiral methane derivatives CFXYZ (X,Y,Z= H, Cl, Br, I) are in the mHz range and below the detection limit. Our research group is therefore searching for molecules including heavy elements (because of the PV Z5-scaling) to achieve enhanced PV effects in the Hz range. New promising candidates are presented in collaboration with the French PV initiative, which aims at a 100 mHz resolution in Ramsay-Fringes experiments using quantum cascade lasers. Another future alternative is single-molecule spectroscopy in traps at ultra-cold temperatures.

Title of seminar: From Meyer and Mendeleev to Oganessian and Dirac: What next after the superheavies and is there an end in sight for the Periodic Table?

Abstract:

The first periodic table of elements was proposed by Dmitri Ivanovich Mendeleev in 1869. It was based on arranging the elements in ascending order of atomic weights and grouping for similarities in chemical properties. Mendeleev predicted the existence and properties of new elements and pointed to accepted atomic weights that were flawed. At this time, it was not known how far one can increase the atomic weight to the critical point where heavy elements become unstable and undergo radioactive decay or when electronic levels dive into the Dirac sea. A century later it was speculated that the periodic table would end with heavy atomic nuclei containing no more than 100 protons because of the immense Coulomb repulsion between the protons. In 1948, however, Goeppert-Mayer pointed out that the nuclear shell model can significantly increase the stability of the atomic nuclei, and Meldner demonstrated in 1967 that the next proton-neutron-shell closure (island of nuclear stability) will take place
at a nuclear charge of Z = 114 and a neutron number of N = 184. Over the past two decades, we gained detailed insight into the nuclear stability problem by producing new superheavy elements up to a nuclear charge of Z = 118 (oganesson). The periodic table is most fundamental to chemistry, but key questions remain unanswered: where does the periodic table end from a theoretical and practical point of view? Can we still do chemistry with exotic and highly unstable elements? How can one predict the chemical and physical behaviour of these superheavy elements as the electronic spectrum becomes dense? What is quantum theory doing in the super-critical Coulomb field region when electronic states dive? Do
superheavy elements exist in nature, and are these produced in supernova explosions or neutron star mergers?

Title of seminar: Observation of entanglement in a cold atom analog of cosmological preheating

Abstract:

Parametric resonance is a universal phenomenon that arises across all scales, from Faraday waves in a water container to particle creation in the early Universe. (Quasi)particles are created in pairs of opposite momenta, and their exponential growth is triggered by fluctuations, such as thermal noise. However, if the initial mean number of (quasi)-particles is zero, vacuum fluctuations initiate the growth, yielding an entangled state. In this seminar, I will report on the experimental parametric creation of opposite-momentum quasi-particles in a Bose-Einstein condensate, and on the evolution of their number and entanglement. This experimental observation is made possible by the introduction of a novel entanglement criterion, to relate number correlation function to entanglement.

There should furthermore be, tomorrow thursday, the next presentation in the series by Peter Schwerdtfeger. Let’s enjoy our summer science camp and come in force to both!