How does the crust of a neutron star transmit heat? How did entropy waves propagate and decay under such extreme physical conditions in the early days of the Big Bang? Why are extremely thin and extremely cold ultracold atoms used to study these dense and hot substances? And how do we listen to their whispers and outpourings?
Pan Jianwei, Yao Xingcan, Chen Yuao, and others from the University of Science and Technology of China collaborated with Australian scientist Hu Hui to measure the attenuation rate of the second sound wave for the first time in a Fermi superfluid at the limit of strong interaction (unit positive), revealing that there is a considerable phase transition critical zone in the system, and obtaining the viscosity coefficient and thermal conductivity that tend to the limit of quantum mechanics. This work provides important experimental information for understanding the phenomenon of quantum transport in strongly interacting Fermi systems, and is an example of using quantum simulation to solve important physical problems. On February 4, the results were published in the form of a long article in the form of an international authoritative academic journal Science [Science 375, 528-533 (2022)].
Quantum simulation
Unlike macroscopic phenomena, it is quantum mechanics that describes the laws of physics in the microscopic world. A system consisting of a large number of microscopic particles that follow quantum mechanics is called a quantum multibody system, and a problem related to the nature and behavior of a quantum multibody system is called a quantum multibody problem. This is a large class of important physical problems, including the mechanism of high-temperature superconductivity, the evolution of the universe in the early days of its birth, and so on. In quantum multibody problems, when the interaction between microscopic particles is relatively weak, the analytical method still has a battle; once the interaction is strong, not only is the analytical solution difficult, but the numerical simulation method based on classical computers is also stretched out - because as the number of particles increases, the resources required for computation will increase geometrically. Then, we might as well "use magic to defeat magic" and use the spear of nature to attack nature's shield; this is the original intention of quantum simulation.
Quantum simulation, as the name suggests, "quantum" means that the basic law involved is quantum mechanics, and "simulation" means to construct and study a problem that is similar in nature to the original problem but is easier to solve. A well-known example of "simulation" is the wind tunnel – when designing the shape of a flying machine, the wind tunnel experiment is a simulation of a real aerodynamic problem. The reason why quantum simulations are highly expected is because quantum mechanics in principle gives simulation methods unique conditions. In quantum mechanics, there is a crucial physical quantity called a Hamiltonian quantity—the nature and evolution of a quantum system is dominated by its Hamiltonian quantity. Therefore, if the Hamiltonian quantities of two quantum multibody systems are indistinguishable, then once we study one of the systems clearly, we can know the properties and behavior of the other system. This sincerity can be described as "defeat is also quantum, and success is also quantum" is also.
What we want to introduce in detail today is to use quantum simulation methods to study a quantum multibody system, the strong interaction Fermi superflow.
BCS-BEC crosses the Fermi supercurrent with strong interaction
In 1911, the Dutch scientist Heike Kamerlingh Onnes (1853-1926) discovered the phenomenon of superconductivity, opening a new chapter in cryogenic physics. Another milestone in cryogenic physics was the first discovery of overcurrent phenomena in liquid helium-4 by the Soviet physicist Kapicha (Пётр Леонидович Капица, 1894-1984). Liquid helium superflow has a series of peculiar properties, such as: it can pass through very fine capillaries without showing any viscosity; it has a very high thermal conductivity, about 800 times that of copper at room temperature; it can overcome gravity and continuously climb up the vessel wall; it can produce a quantized vortex lattice; the existence of a second sound wave that will be highlighted later; and so on. The famous Soviet physicist Lang Dao (Лев Дави дович Ланда у, 1908-1968) established a dihydrofluid model that explained the many properties of liquid helium superflow well from a macroscopic perspective. The two-fluid model holds that liquid helium superfluids contain two components, one is a conventional fluid component with viscosity and entropy, and the other is an overcurrent component, non-viscous and zero entropy. It is the presence of superflow components that makes superfluidics so distinctive. Both superflow and superconductivity are macroscopic quantum effects, and the two are inextricably linked—for example, from some point of view, the superconductivity phenomenon in conventional superconductors can be seen as the result of a large number of electrons forming superflows. To this day, superflow and superconductivity are still hot spots and frontiers in physics research.
The liquid helium that climbs up along the wall of the vessel and then overflows
Microscopic particles in nature can be divided into two categories: fermions and bosons, protons and electrons belong to fermions, and helium-4 and sodium atoms belong to bosons. Two multibody systems composed of two not identical fermions have a variety of physical phenomena, for example, superconductivity is closely related to two systems composed of electrons with different spins. In 1957, John Bardeen (1908-1991), Leon Cooper (1930-), and John Robert Schrieffer (1931-2019) formally proposed the principle of superconductivity, which became known as BCS theory, and explained the experimental results of conventional superconductors almost perfectly. BCS theory points out that one of the keys to superconductivity is the pairing of electrons; as for non-traditional superconductors that cannot be quantitatively described by BCS theory, such as copper-based superconductors, the existence of electron pairing is still the consensus of the scientific community. In fact, electronic pairing is a special case of fermion pairing. Boson-related theories, on the other hand, were born much earlier and far ahead of experiments. Around 1924, Einstein was inspired by Bose to develop what would later be known as Bose-Einstein statistics, and pointed out that a system composed of all bosons would have macroscopic particles occupying the ground state of the system when the temperature was low enough, a phenomenon that was later called Bose-Einstein Condensate (BEC). It wasn't until 1995 that the research team of Eric Cornell and Carl Wieman at the University of Colorado in the United States prepared the first "real" Bose-Einstein condensate.
Pairing of two fermions in bcs-BEC crossings
BCS superflow and Bose-Einstein condensation seem to be unrelated, but in fact they can be incorporated into a unified theoretical framework - BCS-BEC crossing. For a multibody system consisting of two not identical fermions, there is an equivalent weak attraction between the two fermions at the BCS limit, which in turn occurs long-range pairing and superflow; at the BEC limit, the two fermions are paired in a short distance, combined into bosons, and then Bose-Einstein condensation occurs. By modulating the interactions between particles, a smooth transition from bcS superflow to Bose-Einstein condensation can be achieved. Although the theory of BCS-BEC crossing has been proposed more than fifty years ago, it was not until twenty years ago that the development of ultracold atom technology made relevant experimental research possible.
In the middle of the BCS-BEC crossing, there is a very special existence - the strong interaction Fermi system. A strong interaction Fermi system in a state of overcurrent is called a strong interaction Fermi superflow. The reason for the name "strong interaction" is that the interaction between the two fermions that make up the multibody system is so strong that it has reached the upper limit allowed by the two-body scattering theory of quantum mechanics, the unitary limit. In view of this, the strong interaction Fermi system is also known as the monogrammatic system. An important manifestation of this strong correlation is that the relative phase change temperature of the strong interaction Fermi supercurrent (the ratio of the supercurrent/superconducting phase change temperature to the Fermi temperature) is very large, thousands of times that of conventional superconductors, and even much higher than high-temperature superconductors such as copper-based superconductors. The study of strong interaction Fermi superflows will be useful for us to understand and explore strongly correlated Fermi systems such as high-temperature superconductors. Another high-profile feature of the strong interaction Fermi system is that the universality caused by scale invariance - internal energy, entropy and other thermodynamic state functions, as well as viscosity coefficients, thermal conductivity and other transport coefficients are only a function of particle number and temperature, regardless of the specific form of interaction between particles.
Universality is both interesting and useful. In the universe, neutron stars are stars with a density second only to black holes, and if the Earth is compressed to the same density as neutron stars, then the radius of this "Earth" will be only 22 meters. In particular , the crust of a neutron star is a strongly interacting Fermi system. In addition, modern cosmological theory suggests that within a few microseconds after the Big Bang, the universe was filled with extremely hot quark-gluon plasma, a form of matter that can also be considered a strongly interacting Fermi system. And the strongly interacting Fermi gas, which we'll cover next, through ultracold atomic technology, is at the opposite extreme in density and temperature— one millionth of a millionth of air, and only one ten-millionth of a degree Celsius higher than absolute zero. Although the three may seem to be incompatible, with the help of the universality of the strong interaction Fermi system, once we have insight into the nature of one of them, we have a deep understanding of the other two systems. In other words, any one of the three systems can be thought of as a quantum simulation of the other two systems. Neutron stars are unattainable, and the preparation of quark-gluon plasma is not only very difficult, expensive, and extremely short-lived. Therefore, ultra-cold strong interaction Fermi gas is the best candidate for experimental research.
Temperature waves of strong interaction Fermi overcurrents and their attenuation
In a system in a thermodynamic equilibrium state to introduce a small disturbance, so that its temperature is no longer uniform but not change dramatically, if there is no macroscopic particle flow at this time and thermal radiation can be ignored, then heat transfer is the main way of heat transfer in the system. Heat transfer is a special case of diffusion phenomena that follow the diffusion equation. Diffusion phenomenon can be seen everywhere in life, such as dropping a drop of ink in a cup of clear water, and the change of ink droplets in clear water belongs to diffusion. The wave equation, while somewhat similar in mathematical form to the diffusion equation, describes a very different type of phenomenon— volatility. The ripples on the surface of the lake, the monstrous waves on the sea, the noise of the traffic, the colorful neon lights, the sound of wind and rain reading, and the increasingly inseparable wireless network... These are all volatility phenomena. Diffusion and fluctuations are not only crucial in classical physics, but also in quantum multibody systems.
The diffusion of the ink droplets and the fluctuations of the water surface
More than eighty years ago, when landau established a two-fluid model of liquid helium superflow, he pointed out that there are not only what is commonly called sound waves, that is, fluctuations in density, but also fluctuations in temperature, which are also fluctuations in entropy, and call this wave that resembles sound waves the second sound wave. For general substances, such as liquid helium in the conventional fluid phase, slightly uneven temperatures cause heat to propagate in a diffuse manner until the system reaches equilibrium; but in liquid helium in the superluid phase, small inhomogeneities in temperature can propagate in the form of fluctuations. Landau's prediction of a second sound wave was later confirmed experimentally. Is the same superfluid, strong interaction Fermi superflow still described by the difluid model? Is there still a second sound wave? The answer to the first question is not obvious, and the path of exploration of the second question is full of twists and turns. In 2005, scientists experimentally confirmed the presence of a super-fluid phase in ultracool strong interaction Fermi gases,[1] but it was not until 2013 that the presence of a second sound wave was first observed.[2] Directly detecting small fluctuations in temperature in strongly interacting Fermi superflows is unattainable, but fortunately, temperature waves are coupled to a certain degree with density waves. However, this coupling is weak after all, so that the signal of the second sound wave is easily drowned in a sea of noise.
Density fluctuations (ΔP) and temperature fluctuations (ΔT) in overcurrent, n represents conventional fluid components, and s represents overcurrent components
（图源 Russell J. Donnelly, The two-fluid theory and second sound in liquid helium, Physics Today 62(10), 34-39, 2009）
In reality, sound waves also decay during propagation, and for planar waves in uniform media, the attenuation mechanism can be mainly attributed to the diffusion of heat and particle momentum. Thermal conductivity characterizes the diffusion of heat within the system, or heat conduction; the diffusion of particle momentum is closely related to the viscosity of the fluid, and the physical quantity that characterizes this property is called viscosity coefficient, also known as viscosity. The experience of daily life tells us that oil appears slimy compared to water; if we use "physical" terms, the viscosity coefficient of oil is greater than that of water. Since the attenuation of sound waves is associated with both heat conduction and viscosity, the measurement of the attenuation rate of sound waves will provide information about the thermal conductivity and viscosity coefficient of the system.
For fluids with different viscosities (viscosity coefficients), the viscosity of the water in the left figure is much smaller than that of the honey in the right figure
(Image source sciencenotes.org)
As a unique presence among superflows, the propagation and attenuation of the second sound wave can also help us study the critical phenomenon of supercurrent phase transitions. Physically, phase transitions are divided into two categories: first-order phase transitions and continuous phase transitions. The phase transition between the solid phase and the liquid phase, the phase transition between the gas phase and the liquid phase below the critical point are all first-order phase transitions, and the phase transition between ordinary conductors and conventional superconductors and between conventional fluids and superfluids are all continuous phase transitions. Continuous phase transitions have a critical region near the critical point, and scale theory suggests that for systems in critical regions, divergent correlation lengths lead to singularity of many thermodynamic functions, and that the relationship between these singularities is universal. Kinetic scale theory is dedicated to studying the dynamic properties of the system in the critical region such as viscosity, heat conduction, and linear response, which can improve our understanding of the critical phenomenon of continuous phase transition. However, whether it is high-temperature superconductivity or liquid helium superflow, its critical region is relatively narrow, which is not conducive to the experimental study of its critical dynamics. Fortunately, ultracool atomic systems have excellent controllability and are expected to achieve a wider critical region of super-fluid phase transition, and the study of the propagation and attenuation of the second sound wave will also provide impetus for the development of kinetic scale theory.
Although the second sound wave of the strongly interacting Fermi superflow has been observed, due to the experimental techniques of the time, the density of the system in equilibrium is uneven, which hinders the definition and quantitative study of acoustic attenuation [2]. In the past four or five years, the strong interaction Fermi superflow with uniform density has been prepared; in the past two years, the attenuation of its first sound wave has been quantitatively studied [3]. However, the number of particles in the system is small and the Fermi energy is low, so the frequency of the second sound wave is very small, which puts forward extremely harsh requirements for the energy resolution of the experimental device. At this point, not to mention its decay, even the observation of the second sound wave itself becomes difficult.
After more than four years of hard work, the research team composed of Pan Jianwei, Yao Xingcan, Chen Yuao and others of the University of Science and Technology of China has built a new ultra-cold lithium-dysprosium atom quantum simulation platform, integrated and developed many leading ultra-cold atomic regulation methods, such as gray optical viscose, algorithm cooling, three-dimensional cassette-type photostatic well, etc., and finally successfully realized the world's top level of uniform Fermi gas preparation technology. The strongly interacting Fermi superflow prepared on this basis consists of about 10 million Fermi atoms, and the Fermi can reach 50 kHz, which is about 1 order of magnitude higher than the reported results of other research groups in the world. In addition, the control accuracy of the strong interaction Fermi overcurrent has also reached a very high level, for example, the control accuracy of the temperature is better than 0.01 times the Fermi temperature, the non-uniformity of the density is less than 2%, the heating rate of the system is suppressed to a negligible level, and so on. On this basis, through a novel detection method - low momentum transfer (about 0.05 times ferometer momentum) and high energy resolution (better than 0.001 fermone energy) of the Bragg spectroscopy technology, the density response function of the system at the long wave limit can be directly quantitatively observed experimentally. Combining leading preparative techniques and probing techniques, the research team successfully observed the signal of the second sound wave in the density response of the strongly interacting Fermi superflow. Then, by changing the frequency of the system temperature and the Bragg lattice, the density response spectrum of the strong interaction Fermi superflow was measured completely and meticulously, and the experimental results were highly consistent with the fitting curve based on the dissipative difluid model.
(a) Schematic diagram of the experimental apparatus;
Signals from the first sound wave (left) and the second sound wave (right) in the strongly interacting Fermi superflow
Further, the research team of the University of Science and Technology of China, in collaboration with Professor Hu Hui of Swinburne University of Technology, not only quantitatively obtained the sound velocity and attenuation rate of the first and second sound waves of the strong interaction Fermi superflow near the superluid phase transition on the basis of the dissipative difluid model, but also verified the equation of state of matter of the strong interaction Fermi superflow, and even obtained a superfluid fraction that is more accurate than the previous measurements. More importantly, the two transport parameters of viscosity coefficient and thermal conductivity are extracted independently and are close to the limits imposed by quantum mechanics. These limit values are determined only by Planck's constant, Boltzmann's constant, and the density and mass of the particles, independent of other details of the system, and are a manifestation of universality. In addition, experimental results show that the contribution of viscosity and heat transfer to the attenuation of sound waves is equally important. These results provide important experimental information for our in-depth study of other morphologies of strongly interacting Fermi superflows (e.g., neutron star crust, quark-gluon plasma), and even other strongly correlated Fermi systems (e.g., unconventional superconductors), making this work an example of using quantum simulations to study important physical problems. Another surprising gain is that the critical region of the strong interaction Fermi superflow prepared in this work is about a hundred times wider than that of the liquid helium superflow, and such a wide superfluid phase transition critical region combined with excellent temperature control accuracy will provide a good basis for future observation of abnormal transport phenomena near the critical point of phase transition, the measurement of dynamic scale functions, and the development of dynamic scale theory.
Swipe up to read
X. Li, X. Luo, S. Wang, K. Xie, X.-P. Liu, H. Hu, Y.-A. Chen, X.-C. Yao & J.-W. Pan, Second sound attenuation near quantum criticality, Science 375, 528–533 (2022).
Other references
[1] M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck & W. Ketterle, Vortices and superfluidity in a strongly interacting Fermi gas, Nature 435, 1047 (2005).
[2] Leonid A. Sidorenkov, Meng Khoon Tey, Rudolf Grimm, Yan-Hua Hou, Lev Pitaevskii & Sandro Stringari, Second sound and the superfluid fraction in a Fermi
gas with resonant interactions, Nature 498, 78 (2013).
[3] Parth B. Patel, Zhenjie Yan, Biswaroop Mukherjee, Richard J. Fletcher, Julian Struck, Martin W. Zwierlein, Universal sound diffusion in a strongly interacting Fermi gas, Science 370, 1222–1226 (2020).
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