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arXiv:1008.0240

The p=0 condensate is a myth

Yatendra Singh Jain

Published Aug 2, 2010• 5 citations
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Abstract

Analyzing some of the basic aspects of the dynamics of two bosons (interacting through a central force) and their importance in determining the ground state of a system like liquid $^4He$, it is unequivocally concluded that our conventional belief in the existence $p=0$ condensate in the superfluid state of such systems [including the state of Bose Einstein condensate (BEC) of trapped dilute gases] is a myth.

DOI
10.48550/arxiv.1008.0240

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Analyzing some of the basic aspects of the dynamics of two bosons (interacting through a central force) and their importance in determining the ground state of a system like liquid 4He^4He4He, it is unequivocally concluded that our conventional belief in the existence p=0p=0p=0 condensate in the superfluid state of such systems [including the state of Bose Einstein condensate (BEC) of trapped dilute gases] is a myth.
We conclude our study of superfluidity in Bose liquids with a brief summary of the strengths, and of the inadequacies, of the theory. The cornerstone of our fundamental understanding of superfluidity has been the recognition of the central importance of the condensate, a single quantum state which is macroscopically occupied. For the Bose liquid one has a particle condensate, characterized by a non-vanishing expectation value of ψ (r). The existence of the condensate explains all major aspects of superfluid behavior; in particular, we now possess: A clear understanding of the static and the long wavelength dynamic properties of an equilibrium Bose liquid, including a microscopic basis for the two-fluid model. A precise microscopic theory at T = 0 for a specific model, the dilute Bose gas. Variational calculations of the excitation spectrum of liquid He II (and of the ground state properties as well), which are in good quantitative agreement with experiment. A satisfactory phenomenological treatment of the interactions between elementary excitations which give rise to various irreversible phenomena. A qualitative understanding of the role which is played by quantized vortices in both equilibrium and non-equilibrium phenomena.
Analyzing the basic dynamics of two bosons, interacting through a central force, we make three unequivocal conclusions: (i). Natural laws, demanding the ground state of a system to have least possible energy, forbid the existence of p = 0 condensate in a system of interacting bosons (SIB). (ii). The ground state of a SIB, with different number of particles having different momenta does not have least possible energy as it should be. (iii). All particles in the true ground state have identically equal energy, εo = h2/8md2, and equivalent momentum, qo = π/d. The real nature of Bose Einstein condensation (BEC) that exists in the superfluid state of a SIB is identified as the condensation of particles in a state of a pair of particles having equal and opposite momenta (q, -q) with center of mass momentum, K = 0 and q = π/d. We also discuss how experimental results pertaining to the existence of electron bubble and free rotation of molecules in helium droplets and clusters support the absence of p=0 condensate and how single particle basis (SPB), having an alliance with p=0 condensate, is inconsistent with certain physical realities of the system at low temperatures. These conclusions render strong support for our theory of superfluidity of a system like liquid 4He (Amer. J. Cond. Mat. Phys. 2, 32-52(2012).
Since the early days of Bose–Einstein condensates (BECs) in atomic gases, comparisons have been drawn to the other familiar bosonic systems: liquid helium-4 and the Cooper pairs of superconductors. Two of the early questions asked of BECs were whether they had similar coherence properties and whether they were superfluids. In He4, it is rather difficult to study properties of the condensate, such as the condensate fraction, whereas the measurement of superfluidity is fairly straightforward. The opposite has proved true for atomic condensates: The condensate fraction as a function of temperature was found early on, but only recently has their superfluidity been placed on firm footing (see PHYSICS TODAY, November 1999, page 17).
Experimental observation of superfluidity in a microscopic cluster, M:(4He)xM:(^4He)_xM:(4He)x​, of a molecule (MMM) and xxx number of 4He^4He4He atoms (with xxx ranging from 1 to many) is qualitatively analyzed. It concludes that: (i) each 4He^4He4He atom in the cluster has to have non-zero momentum for its confinement to a space of size ($
This chapter presents an overview of the specific experimental tools developed in the field of ultra-cold gases to achieve and probe superfluidity in vapours of bosonic atoms. First, it describes the main cooling techniques: the magneto-optical trap, which brings an atomic vapour from room temperature down to the sub-mK range, and the evaporative cooling scheme, which bridges the gap to the superfluid regime. It then proceeds to the study of interaction effects. It shows that these play a central role in the understanding of both static and dynamic properties of trapped Bose–Einstein condensates (BECs), despite the dilute character of these gases. As a consequence, gaseous BECs and superfluid helium obey the same laws of hydrodynamics and exhibit similar dynamical properties, although their densities differ by several orders of magnitude. The third section is devoted to the coherence properties of gaseous BECs. It shows that, by contrast with liquid helium, specific features of ultra-cold gases make them suitable for a direct probing of the quantum coherence associated with Bose–Einstein condensation. Finally, the possibility of tailoring trapping potentials and realizing low-dimensional systems is discussed, where one or two directions of motion are frozen.