M. Grether

Bose-Einstein condensation in the relativistic ideal Bose gas

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is lower with antibosons, thus implying that omitting antibosons always leads to the computation of a metastable state.

Low-dimensional BEC

The Bose-Einstein condensation (BEC) temperature Tc of Cooper pairs (CPs) created from a general interfermion interaction is determined for a linear, as well as the usually assumed quadratic, energy vs center-of-mass momentum dispersion relation. This explicit Tc is then compared with a widely applied implicit one of Wen & Kan (1988) in d=2+∈ dimensions, for small ∈, for a geometry of an infinite stack of parallel (e.g., copperoxygen) planes as in, say, a cuprate superconductor, and with a new result for linear-dispersion CPs. The implicit formula gives Tc values only slightly lower than those of the explicit formula for typical cuprate parameters.

Planck-scale effects on Bose-Einstein condensates

The effects of a Planck-scale deformation of the Minkowski energy-momentum dispersion relation on the phenomenology of non-trapped Bose-Einstein condensates (BECs) are examined. Such a deformation is shown to cause a shift in the condensation temperature Tc of the BEC and, for a specific functional form of deformation, this shift can be as large as the current measured precision on Tc. For a 8537Rb cold-atom BEC with a particle density n1012cm−3 we find a fractional shift of order 10−4, but this can be much larger for even more dilute BECs. We discuss the possibility of planning specific experiments with BECs that might provide phenomenological constraints on Planck-scale physics. These corrections to Tc are found to be extremely small for ultrarelativistic BECs implying that, in some cases, Planck-scale effects may be more important in low- rather than high-energy processes.

INTRIGUING ROLE OF HOLE-COOPER-PAIRS IN SUPERCONDUCTORS AND SUPERFLUIDS

The role in superconductors of hole-Cooper-pairs (CPs) are examined and contrasted with the more familiar electron-CPs, with special emphasis on their “background” effect in enhancing superconducting transition temperatures Tc — even when electron-CPs drive the transition. Both kinds of CPs are, of course, present at all temperatures. An analogy is drawn between the hole CPs in any many-fermion system with the antibosons in a relativistic ideal Bose gas that appear in substantial numbers only at higher and higher temperatures. Their indispensable role in yielding a lower Helmholtz free energy equilibrium state is established. For superconductors, the problem is viewed in terms of a generalized Bose-Einstein condensation (GBEC) theory that is an extension of the Friedberg-T.D. Lee 1989 boson-fermion BEC theory of high-Tc superconductors in that the GBEC theory includes hole CPs as well as electron-CPs — thereby containing as well as further extending BCS theory to higher temperatures with the same weak-coupling electron-phonon interaction parameters. We show that the Helmholtz free energy of both 2e- and 2h-CP pure condensates has a positive second derivative, and are thus stable equilibrium states. Finally, it is conjectured that the role of hole pairs in ultra-cold fermionic atom gases will likely be negligible because the very low densities involved imply a “shallow” Fermi sea.

Harmonically trapped ideal quantum gases

Abstract:We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature Tc if and only if d + δ > 2, along with a jump in the specific heat at Tc if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases 3787Rb, 37Li, 3785Rb, 24He, 1941K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for 1127Na and 11H.

Long-range order Hartree-Fock states with different magnetic properties

The Hartree-Fock (HF) energies of a new set of HF orbitals with long-range order are calculated for two different models which involve a system of many fermions interacting via repulsive delta potentials as a preliminary step facing such problems as the electron gas system, 3He systems, etc., where, however, the calculation of the relevant matrix elements is considerably more difficult. The models considered illustrate paramagnetic and antiferromagnetic behaviour. The authors find a whole new set of HF orbitals which are more stable than the (trivial) plane wave orbitals as well as the classic Overhauser ones.

Rapid fabrication of on-demand high-resolution optical masks with a CD-DVD pickup unit

A low-cost, direct fabrication technique with a micrometer range resolution has been implemented for rapid prototyping of optical masks for photolithography and structured light and diffraction optics applications. Using a setup based on the optical unit of a compact disc-digital versatile disc burner, a low-energy infrared laser beam was focused on a thin polymeric layer with embedded absorbing carbon nanopowder coated on a transparent glass substrate. This allowed for the generation of a custom-made transparent pattern in a computer numerical control fashion. In addition to its great simplicity and repeatability, the method also enables grayscale contrasts for each pixel individually, and fabricated masks proved to resist high intensities.

The Hong–Ou–Mandel interferometer in the undergraduate laboratory

The Hong?Ou?Mandel interferometer is an optical device that allows us to prove the quantum nature of light experimentally via the quantum amplitude superposition of two indistinguishable photons. We have implemented this experiment as an advanced undergraduate laboratory experience. We were able to overcome well-known difficulties using techniques reported recently by Thomas et al (2009 Rev. Sci. Instrum. 80 036101).

Origin of a nonlinear contribution to the shift of the critical temperature in atomic Bose-Einstein condensates

We discuss a possible origin of the experimentally observed nonlinear contribution to the shift ΔTc = Tc − Tc0 of the critical temperature Tc in an atomic Bose-Einstein condensate (BEC) with respect to the critical temperature Tc0 of an ideal gas. We found that accounting for a nonlinear (quadratic) Zeeman effect (with applied magnetic field closely matching a Feshbach resonance field B0) in the mean-field approximation results in a rather significant renormalization of the field-free nonlinear contribution b2, namely, Tc/Tc0 ≃ b2* (a/λT)2 (where a is the s-wave scattering length, λT is the thermal wavelength at Tc0) with b2* = γ2b2 and γ = γ(B0). In particular, we predict b2* ≃ 42.3 for the B0 ≃ 403 G resonance observed in the 39K BEC.

Is Room‐temperature Superconductivity with Phonons Possible?

By recognizing the vital importance of two‐hole Cooper pairs (CPs) in addition to the usual two‐electron ones in a strongly‐interacting many‐electron system, the concept of CPs was re‐examined with striking conclusions: namely, they are gapped and linearly‐dispersive resonances with a finite lifetime—but provided the ideal‐gas Fermi sea is replaced by a BCS‐correlated unperturbed ground‐state “sea.” Based on this, Bose‐Einstein condensation (BEC) theory has been generalized to include not boson‐boson interactions (also neglected in BCS theory) but rather boson‐fermion (BF) interaction vertices reminiscent of the Frohlich electron‐phonon interaction in metals. Instead of phonons, the bosons in the generalized BEC (GBEC) theory are now both particle and hole CPs. Unlike BCS theory, the GBEC model is not a mean‐field theory restricted to weak‐coupling as it can be diagonalized exactly. In weak coupling it reproduces the BCS condensation energy, and the next‐order‐in‐coupling term increases its magnitude with...