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Simulations and Symmetries: Cold Atoms, QCD, and
Fewhadron Systems
(INT program March 15  May 21, 2010)
Reported by: Daniel Phillips (Ohio U),
HansWerner Hammer (U Bonn), and Martin Savage (U Washington)
Date posted August 9, 2010
Rapid advances in the experimental study of systems of cold atoms have provided controlled environments in which to explore quantum manybody dynamics. In particular, the ability to trap atoms, and dictate the strength of their interaction through Feshbach resonances, has provided a laboratory with which to investigate the consequences of varying scattering lengths all the way from the range of the atomatom interaction to infinity. When the atomatom scattering length is infinite the resulting system is "unitary", as atomatom scattering saturates the bound imposed by the conservation of probability. In this limit the manybody quantum system has scaleinvariance for length scales larger than the range of the twobody interaction, and this leads to the existence of "universal" properties, which do not depend on the underlying force. A famous example of the implications of a unitary atomatom interaction is found in the spectrum of particular threeatom systems. As predicted by Efimov long ago, the spectrum of such systems has states that are simply scaled copies of each other with energies that are multiplicatively related. This is now understood in the language of the renormalization group as resulting from an infrared limitcycle. In the last few years it has further been discovered that the underlying scaling symmetry impacts the structure of systems composed of more than three bodies, as illustrated in Figure 1. Figure 1. Fourbody Efimov states built upon threebody Efimov states. [Image taken from C. Greene's program presentation "Universality and the Efimov effect".] The relation between systems near unitarity and nuclear physics is that the parameters of quantum chromodynamics (QCD) are such that the swave nucleonnucleon interaction produces scattering lengths that are much larger than the range of the interaction. The triton is then "close" to having a second state, which would be identified as an Efimov state, and it has been conjectured that lightquark masses would need to change only slightly from their values in nature to produce this Efimov state. Lattice QCD is the calculational tool with which this could be definitively explored, but, presently, the only practical tool available to map out the lightquark mass dependence of nuclear processes is effective field theory (EFT). To be reliable such an EFT has to build in the finetuning inherent in the nucleonnucleon scattering lengths, and the role of the important lowenergy scales of QCD.
Systems near Unitarity Meanwhile, the last few years saw the first theoretical predictions for fourbody loss features in cold atomic gases at or near unitarity. These have recently been validated in experiments by groups at Innsbruck and Rice Universities. This confirms that a fourbody interaction is not required to define a fourbody system of bosons interacting via shortrange forces alone. New universal predictions for that system, such as those shown in Figure 1, are the result. Comparisons between such predictions for the fourbody system and experimental measurements in the controlled environment of a cold atomic gas are ongoing, and promise to reveal much about fourparticle quantum dynamics.
From QCD to light nuclei, via modern nuclear interactions "Halo" nuclei such as Helium6 and Helium8 are a particular challenge in this last regard, since the final few neutrons in these systems are bound by much less than the average binding energy per nucleon in typical nuclei. Ab initio calculations are overcoming the challenges, and making important progress towards quantitative description of these systems. Good agreement is now found with the very precise chargeradius numbers obtained from laser spectroscopy of Helium6 and Helium8 atoms (see Figure 2). Figure 2. Artist's impressions of neutron distribution (blue) and proton distribution (red), as well as measured charge radii, for Helium4, Helium6, and Helium8 isotopes. [Image taken from P. Mueller's program presentation, "Laser trapping and probing of exotic Helium isotopes".] Halo nuclei are fascinating systems partly because they provide another connection to physics near unitarity. Similarities and differences between the swave fewbody systems near unitarity discussed above and systems with resonant pwave clusterneutron interactions (e.g. Helium6 and Helium8) are under investigation, with a particular focus on whether the latter display "universal properties" similar to those found in systems with resonant swave interactions.
Nuclear Physics from Lattice QCD What would seem to be a straightforward task for lattice QCD is the calculation of the nucleonpion scattering phaseshift in the Deltaisobar region, and the subsequent identification of the pole and width of the Delta (analogously, similar calculations for other unstable hadrons such as the rho meson, as shown in Figure 3). The recent work by the QCDSF collaboration makes clear the extent of the difficulties of such calculations, and that calculations in big enough volumes will require significantly larger computational resources than have been used to date. Figure 3. The π π phase shift versus pion momentum in the vicinity of the ρresonance. The right curve corresponds to a π mass of 250 MeV, while the left one if for a π mass of 390 MeV. [QCDSF collaboration, PoS LATTICE2008: 136,2008, ePrint: arXiv:0810.5337 [heplat].] This is just one example where knowing the expected energyspectrum of fewhadron systems placed in finite volumes is key to developing an understanding of what we can expect in future lattice QCD calculations. It is anticipated that the spectrum beyond the nuclear ground state is quite complicated, and so predictions for the spectrum based upon a reliable EFT and modern fewnucleon methods would be very valuable. The usefulness and practicality of different boundary conditions for both Lattice QCD and nuclear manybody calculations are also being thoroughly investigated (as illustrated in Figure 4). The ability to benchmark finitevolume effects using data from trapped atomic systems is very beneficial here. Figure 4. Theoretical and experimental boundary conditions that are imposed upon fewnucleon systems. Lattice QCD calculations are presently restricted to (hyper)cubic volumes with periodic boundaryconditions, while nuclear manybody calculations and atomic experiments use harmonic oscillator potentials. [Image taken from T. Luu's program presentation "Nuclear Physics within Finite Volumes".] Continued collaboration between lattice QCD and fewbody physics is essential in order to optimally determine the consequences of QCD for nuclear physics.
