We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure and critical behavior. The study identifies the emergence of Goldstone modes and clarifies their role in the low-energy excitation spectrum. The results provide insight into the interplay between symmetry, rotation, and many-body interactions, contributing to a deeper theoretical understanding of phase structures in Bose systems.We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure, critical behavior, and low-energy excitation spectrum. We identify the emergence of Goldstone modes (massless rotons and massive phonons) in the symmetry-broken phase and clarify their role in mediating low-energy excitations—findings that remain robust at low momentum regardless of rotation. A key result is the angular velocity (Ω) dependence of the critical temperature (Tc) for U(1) phase transition, where Tc scales as Ω^(1/3), distinct from the Ω^(2/5) (nonrelativistic) and Ω^(1/4) (ultrarelativistic) scaling observed in noninteracting rotating Bose gases. Rotation also alters the temperature dependence of the thermodynamic potential minima, changing the characteristic factor from (1 - t) (t = T/Tc for nonrotating systems) to (1 - t³) for rotating gases. We further demonstrate that rotation preserves the second-order nature of the phase transition, while modifying the critical exponents and reducing the discontinuity in heat capacity with increasing Ω. Additionally, we define a σ meson dissociation temperature (Tdiss) characterized by mσ(Tdiss) = 2mπ(Tdiss), showing that Tdiss is always lower than Tc. Thermal mass corrections are shown to ensure the validity of Goldstone’s theorem in the rotating frame, even in the chiral limit. These results deepen our understanding of the interplay between symmetry, rotation, and many-body interactions, with implications for interpreting extreme conditions in heavy-ion collisions and compact astrophysical objects, while advancing the theoretical framework for phase structures in rotating Bose systems.
We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure and critical behavior. The study identifies the emergence of Goldstone modes and clarifies their role in the low-energy excitation spectrum. The results provide insight into the interplay between symmetry, rotation, and many-body interactions, contributing to a deeper theoretical understanding of phase structures in Bose systems.We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure, critical behavior, and low-energy excitation spectrum. We identify the emergence of Goldstone modes (massless rotons and massive phonons) in the symmetry-broken phase and clarify their role in mediating low-energy excitations—findings that remain robust at low momentum regardless of rotation. A key result is the angular velocity (Ω) dependence of the critical temperature (Tc) for U(1) phase transition, where Tc scales as Ω^(1/3), distinct from the Ω^(2/5) (nonrelativistic) and Ω^(1/4) (ultrarelativistic) scaling observed in noninteracting rotating Bose gases. Rotation also alters the temperature dependence of the thermodynamic potential minima, changing the characteristic factor from (1 - t) (t = T/Tc for nonrotating systems) to (1 - t³) for rotating gases. We further demonstrate that rotation preserves the second-order nature of the phase transition, while modifying the critical exponents and reducing the discontinuity in heat capacity with increasing Ω. Additionally, we define a σ meson dissociation temperature (Tdiss) characterized by mσ(Tdiss) = 2mπ(Tdiss), showing that Tdiss is always lower than Tc. Thermal mass corrections are shown to ensure the validity of Goldstone’s theorem in the rotating frame, even in the chiral limit. These results deepen our understanding of the interplay between symmetry, rotation, and many-body interactions, with implications for interpreting extreme conditions in heavy-ion collisions and compact astrophysical objects, while advancing the theoretical framework for phase structures in rotating Bose systems.
We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure and critical behavior. The study identifies the emergence of Goldstone modes and clarifies their role in the low-energy excitation spectrum. The results provide insight into the interplay between symmetry, rotation, and many-body interactions, contributing to a deeper theoretical understanding of phase structures in Bose systems.
We study the Bose-Einstein condensation (BEC) of a free Bose gas under rigid rotation. The aim is to explore the impact of rotation on the thermodynamic quantities associated with BEC, including the Bose-Einstein (BE) transition temperature and condensate fraction. We begin by introducing the rotation in the Lagrangian density of free charged Klein-Gordon fields and determine the corresponding grand canonical partition function at finite temperature, chemical potential, and finite angular velocity. Assuming slow rotation, we derive analytical expressions for the pressure, energy, number, and angular momentum densities of a free Bose gas in nonrelativistic and ultrarelativistic limits in terms of the corresponding fugacities. We then focus on the phenomenon of BEC. We calculate the critical temperature of BEC transition and the condensate fraction in a slowly rotating Bose gas including only particles. Our findings indicate that the critical exponent associated with the BE transition in a rotating gas is lower compared to that in a nonrotating Bose gas. We also determine the fugacity in a rotating Bose gas in the aforementioned limits and examine how rotation affects its temperature dependence, both below and above the critical temperature. By analyzing the behavior of heat capacity at these temperatures, we demonstrate that in a nonrelativistic Bose gas, the rotation transforms the nature of the BE phase transition from a continuous to a discontinuous transition. In general, we find that a nonrelativistic Bose gas under rotation behaves similarly to a nonrotating Bose gas in ultrarelativistic limit.
We investigate the physics of a gas of ultracold atoms coupled to three single-mode optical cavities and transversely pumped with a laser. Recent work has demonstrated that, for two cavities, the Z2 symmetries of each cavity can be combined into a global U(1) symmetry [J. L\'eonard et al., Nature (London) 543, 87 (2017)]. Here we show that when adding an extra cavity mode, the low-energy description of this system can additionally exhibit an SO(3) rotational symmetry which can be spontaneously broken. This leads to a superradiant phase transition in all the cavities simultaneously, and the appearance of Goldstone and amplitude modes in the excitation spectrum. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We also obtain the excitation spectrum for each phase and discuss the atomic self-organized structures that emerge in the different superradiant phases. We argue that coupling the atoms equally to n different modes will in general generate a global SO(n) symmetry if the mode frequencies can be tuned to the same value.
In this paper, as a personal review, we suppose a possible extension of Gibbs ensemble theory so that it can provide a reasonable description of phase transitions and spontaneous symmetry breaking. The extension is founded on three hypotheses, and can be regarded as a microscopic edition of the Landau phenomenological theory of phase transitions. Within its framework, the stable state of a system is determined by the evolution of order parameter with temperature according to such a principle that the entropy of the system will reach its minimum in this state. The evolution of order parameter can cause a change in representation of the system Hamiltonian; different phases will realize different representations, respectively; a phase transition amounts to a representation transformation. Physically, it turns out that phase transitions originate from the automatic interference among matter waves as the temperature is cooled down. Typical quantum many-body systems are studied with this extended ensemble theory. We regain the Bardeen–Cooper–Schrieffer solution for the weak-coupling superconductivity, and prove that it is stable. We find that negative-temperature and laser phases arise from the same mechanism as phase transitions, and that they are unstable. For the ideal Bose gas, we demonstrate that it will produce Bose–Einstein condensation (BEC) in the thermodynamic limit, which confirms exactly Einstein's deep physical insight. In contrast, there is no BEC either within the phonon gas in a black body or within the ideal photon gas in a solid body. We prove that it is not admissible to quantize the Dirac field by using Bose–Einstein statistics. We show that a structural phase transition belongs physically to the BEC happening in configuration space, and that a double-well anharmonic system will undergo a structural phase transition at a finite temperature. For the O( N )-symmetric vector model, we demonstrate that it will yield spontaneous symmetry breaking and produce Goldstone bosons; and if it is coupled with a gauge field, the gauge field will obtain a mass (Higgs mechanism). Also, we show that an interacting Bose gas is stable only if the interaction is repulsive. For the weak interaction case, we find that the BEC is a 'λ-transition' and its transition temperature can be lowered by the repulsive interaction. In connection with liquid 4 He, it is found that the specific heat at constant pressure C P will show a T 3 law at low temperatures, which is in agreement with the experiment. If the system is further cooled down, the theory predicts that C P will vanish linearly as , which is anticipating experimental verifications.
Higgs and Goldstone modes manifest as fluctuations in the order parameter of system, offering insights into its phase transitions and symmetry properties. Exploring the dynamics of these collective excitations in a Rydberg atoms system advances various branches of condensed matter, particle physics, and cosmology. Here, we report an experimental signature of Higgs and Goldstone modes in a U(1) symmetry-broken Rydberg atomic gases. By constructing two probe fields to excite atoms, we observe the distinct phase and amplitude fluctuations of Rydberg atoms collective excitations under the particle-hole symmetry. Due to the van der Waals interactions between the Rydberg atoms, we detect a symmetric variance spectrum divided by the divergent regime and phase boundary, capturing the full dynamics of the additional Higgs and Goldstone modes. Studying the Higgs and Goldstone modes in Rydberg atoms allows us to explore fundamental aspects of quantum phase transitions and symmetry breaking phenomena, while leveraging the unique properties of these highly interacting systems to uncover new physics and potential applications in quantum simulation.
We explored interaction cold atoms in new quantum regimes that have no prior analogue in condensed matter materials in three related main topics. First, motivated by recent advance in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a high partial wave interacting Bose gas. Remarkably different from what was previously known in the p-wave case, the atomic superfluid is found to be momentum-independent in the present d-wave case. What is more, we study the quantum fluctuations in the condensates of a mixture of bosonic atoms and molecules with interspecies p-wave interaction. Our analysis shows that the quantum phase of coexisting atomic and molecular condensates is unstable at the mean-field level. The quantum Lee-Huang-Yang correction to the mean-field energy provides a remarkable mechanism to self-stabilize the phase. The correlated order spontaneously breaks a rich set of global U(1) gauge, atomic spin, spatial rotation and translation, and time-reversal symmetries. Second, we study the dynamics of a non-integrable spin chain model composed of two ingredients - a nearest neighbor Ising coupling, and an infinite range XX interaction. Unlike other fast scrambling many-body systems, this model is not known to be dual to a black hole. We demonstrate that our model exhibits fast scrambling for a wide parameter regime, accompanied by a fast growth of the entanglement entropy, as well as a swift change in the magnetization. Third, to extend the study of the highly chaotic many-body model, we analyze the ground state phases of the model with a nearest neighbor XXZ interaction and an infinite range XX interaction. By employing spin-wave theory, we find that there is a large parameter regime where the continuous U(1) symmetry of this model is spontaneously broken, which is not possible in the absence of the infinite range interaction by the Mermin-Wagner theorem. Furthermore, we demonstrate that in the U(1) symmetry broken phase, the half chain entanglement entropy violates the area law logarithmically. Our work demonstrates that the interplay of short and long range interactions can lead to novel quantum phases of matter.