Abstract Identifying possible microscopic mechanisms underlying superfluidity has been the goal of various studies since the introduction of the original BCS theory. Recently a series of papers have proposed microscopic dynamics based on normal modes to describe superfluidity without the use of real-space Cooper pairs. Multiple properties were determined with excellent agreement with experimental data. The group theoretic basis of this general N -body approach has allowed the microscopic behavior underlying these results to be analyzed in detail. This reimagination is now used to reinterpret several interrelated phenomena including Cooper pairs, the Fermi sea, and Pauli blocking. This approach adheres closely to the early tenets of superconductivity/superfluidity which assumed pairing only in momentum space, not in real space. The Pauli principle is used, in its recently revealed role in collective motion, to select the allowed normal modes. The expected properties of superfluidity including the rigidity of the wave function, interactions between the fermions in different pairs, convergence of the momentum and the gap in the excitation spectrum are discussed.
Abstract Identifying possible microscopic mechanisms underlying superfluidity has been the goal of various studies since the introduction of the original BCS theory. Recently a series of papers have proposed microscopic dynamics based on normal modes to describe superfluidity without the use of real-space Cooper pairs. Multiple properties were determined with excellent agreement with experimental data. The group theoretic basis of this general N -body approach has allowed the microscopic behavior underlying these results to be analyzed in detail. This reimagination is now used to reinterpret several interrelated phenomena including Cooper pairs, the Fermi sea, and Pauli blocking. This approach adheres closely to the early tenets of superconductivity/superfluidity which assumed pairing only in momentum space, not in real space. The Pauli principle is used, in its recently revealed role in collective motion, to select the allowed normal modes. The expected properties of superfluidity including the rigidity of the wave function, interactions between the fermions in different pairs, convergence of the momentum and the gap in the excitation spectrum are discussed.
Typically visualized from an independent particle viewpoint, the Pauli principle's role in collective motion is analyzed leading to a reimagination of the microscopic dynamics underlying superfluidity/superconductivity and a reinterpretation of several interrelated phenomena: Cooper pairs, the Fermi sea, and Pauli blocking. The current approach, symmetry-invariant perturbation theory is a first principles method with no adjustable parameters. An adiabatic evolution is employed to transfer the well-known Pauli restrictions for identical, independent particles with two spin values to restrictions on the collective modes of an ensemble of ``spin up'' ``spin down'' particles. The collective modes, analytic N-body normal modes, are obtained from a group theoretic exact solution of the first-order equations. Cooper pairing is reinterpreted not as the pairing of two fermions with total zero momentum, but as the convergence of the momentum of the entire ensemble to two values, +k and -k, as the particles in the normal mode move back and forth with a single frequency and phase. The Fermi sea and Pauli blocking, commonly described using independent fermions that occupy lower states to create a ``sea'' in energy space and block occupation is redescribed as a collective energy phenomena of the entire ensemble. Superfluidity, which has always been viewed as a collective phenomena as Cooper pairs are assumed to condense into a macroscopic occupation of a single lowest state, is now reimagined without two-body pairing in real space, but as a macroscopic occupation of a low-energy phonon normal mode resulting in the convergence of the momentum to two equal and opposite values. The expected properties of superfluidity including the rigidity of the wave function, interactions between fermions in different pairs, convergence of the momentum and the gap in the excitation spectrum are discussed.
The transition from the weakly interacting BCS regime to the strongly interacting unitary regime is explored for ultracold trapped Fermi gases assuming a normal mode description of the gas instead of the conventional Cooper pairing. The Pauli principle is applied ``on paper'' by using specific normal mode assignments. Energies, entropies, critical temperatures, and an excitation frequency are studied and compared to existing results in the literature. These normal modes have been derived analytically for N identical, confined particles from a first-order L=0 group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction. In previous studies, normal modes were able to describe the unitary regime obtaining ground state energies comparable to benchmark results and thermodynamics quantities in excellent agreement with experiment. In a recent study, the behavior of the normal mode frequencies was investigated for Hamiltonians with a range of interparticle interaction strengths from BCS to unitarity in the first test of this approach beyond the unitary regime, and a microscopic basis of the large excitation gaps and universal behavior at unitarity was proposed. Based on the success of these earlier studies, the current paper continues to explore the ability of normal modes to describe superfluidity along the BCS to unitarity transition. The results confirm earlier conclusions that the physics of superfluidity can be described using normal modes across a wide range of interparticle interaction strengths and offer an alternative to the two-body pairing models commonly used to describe superfluidity along this transition.
Understanding the emergence of collective organizational phenomena is a major goal in many fields of physics from condensed matter to cosmology. Using a recently introduced manybody perturbation formalism for fermions, we propose a mechanism for the emergence of collective behavior, specifically superfluidity, driven by quantum statistics and the enforcement of the Pauli principle through the selection of normal modes. The method, which is called symmetry invariant perturbation theory (SPT), uses group theory and graphical techniques to solve the manybody Schrodinger equation through first order exactly. The solution at first order defines collective coordinates in terms of five N-body normal modes, identified as breathing, center of mass, single particle angular excitation, single particle radial excitation and phonon. A correspondence is established "on paper" that enforces the Pauli principle through the assignment of specific normal mode quantum numbers. Applied in the unitary regime, this normal mode assignment yields occupation only in an extremely low frequency N-body phonon mode at ultralow temperatures. A single particle radial excitation mode at a much higher frequency creates a gap that stabilizes the superfluidity at low temperatures. Coupled with the corresponding values for the frequencies at unitarity obtained by this manybody calculation, we obtain good agreement with experimental thermodynamic results including the lambda transition in the specific heat. Our results suggest that the emergence of collective behavior in macroscopic systems is driven by the Pauli principle and its selection of the correct collective coordinates in the form of N-body normal modes.
Abstract Understanding the universal behavior of strongly-interacting systems of particles has been a major goal in multiple fields of physics from atomic physics to cosmology. Using a recently introduced manybody perturbation formalism for fermions which uses group theoretic and graphical techniques to solve the N -body problem, I study the thermodynamic behavior of the unitary regime for a trapped Fermi gas and investigate the role of the Pauli principle in the emergence of collective behavior, specifically superfluidity at ultralow temperatures. The method, which is called symmetry invariant perturbation theory, has no adjustable parameters and currently offers a solution to the manybody Schrodinger equation through first order in inverse dimensionality exactly. The solution at first order defines collective coordinates in terms of five types of N -body normal modes, identified as symmetric stretch, symmetric bend, single particle angular excitation, single particle radial excitation and phonon. A correspondence is established ‘on paper’ that enforces the Pauli principle through the assignment of specific normal mode quantum numbers. Applied at ultracold temperatures, this normal mode assignment yields occupation only in an extremely low frequency N -body phonon mode. A single particle radial excitation mode at a much higher frequency creates a gap that stabilizes the superfluidity at low temperatures. This radial excitation involves excitation of a single particle out of the synced motion of the phonon mode, rather than the breaking of a fermion pair. Coupled with the corresponding values for the energies at unitarity obtained by this manybody calculation, I obtain good agreement with experimental thermodynamic results. In particular, the lambda transition in the specific heat is clearly seen. Based on these findings, I propose a mechanism for the emergence of superfluidity at ultralow temperatures in this unitary regime that is driven by quantum statistics and the enforcement of the Pauli principle through the selection of normal modes. My results for the calculated thermodynamic quantities suggest that the emergence of some collective behaviors in macroscopic systems is due to the Pauli principle producing manybody pairing and the resulting macroscopic occupation of an N -body phonon mode.
The frequencies of the analytic normal modes for N identical particles are studied as a function of system parameters from the weakly interacting BCS regime to the strongly interacting unitary regime. The normal modes were obtained previously from a first-order L=0 group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction for confined identical particles. In a precursor to this study, the collective behavior of these normal modes was investigated as a function of N from few-body systems to many-body systems analyzing the contribution of individual particles to the collective macroscopic motions. A specific case, the Hamiltonian for Fermi gases in the unitary regime, was studied in more detail. This regime is known to support collective behavior in the form of superfluidity and has previously been successfully described using normal modes. Two phenomena that could sustain the emergence and stability of superfluid behavior were revealed, including the behavior of the normal mode frequencies as N increases. In this paper, I focus on a more detailed analysis of these analytic frequencies, extending my investigation to include Hamiltonians with a range of interparticle interaction strengths from the BCS regime to the unitary regime and analyzing the microscopic dynamics that lead to large gaps at unitarity. The results of the present study suggest that in regimes where higher-order effects are small, normal modes can be used to describe the physics of superfluidity from the weakly interacting BCS regime with the emergence of small excitation gaps to unitarity with its large gaps and can offer insight into a possible microscopic understanding of the behavior at unitarity. This approach could thus offer an alternative to the two-body pairing models commonly used to describe superfluidity along this transition.
The zero-point energy of a trapped ultracold Fermi gas at unitarity is investigated in relation to the combined effects of the Heisenberg uncertainty principle and the Pauli principle. This lowest allowed quantum state is a superfluid state which has been studied extensively both experimentally and theoretically. The method used for the current investigation is based on a recent series of papers that proposed microscopic dynamics based on normal modes to describe superfluidity instead of real-space Cooper pairs. This approach yielded excellent agreement with experimental data for multiple properties and allowed the microscopic behavior underlying these results as well as the basis of universal behavior to be analyzed in detail using the group theoretic basis of this general N-body approach. This microscopic picture is now used to illucidate the roles played by the uncertainty principle and the Pauli principle in determining the energy and character of the lowest allowed quantum state including the squeezed character of this superfluid state and the suppression of the Pauli principle.