Questions and some outcomes of the discussion on the week's topics 02/08/13

Please do correct and add - I know that I miss(pell)ed a lot....

Photo of brainstorming topics on blackboard

Q: We had discussed earlier the reasons why OH molecules are so good for our purposes, i.e., why the ratio between elastic and inelastic cross sections is so high. (In short, this is linked to the parameter d4/(delta E), where d is the dipole moment, and delta E the relevant dipolar (closest) level splitting. This delta is the lambda doubling splitting which is very small.) What other molecules do exist which might display such favorable properties?
Discussion: For OD, metastable CO (a3PiOm=1/2,2/3) the situation is very similar, molecules like NH3 (1A1 state with tunneling splitting) have very similar properties.
The question is how far dressing can help to prepare such molecules. Seems to be in principle possible, but yet mostly unexplored. There is, however, considerable expertise on the topic of blue-shielding, which goes in a similar direction. With all these ideas, dimensionality can be a limit.

Q: Efimov physics: Is the (main) interaction just pairwise, or how far do three-body interactions play a role? What do dipolar particles add to the mix? What are the benefits/dangers of having energy-dependent (pseudo-) potentials?
Discussion: First of all, pairwise interaction can clearly explain all observed phenomena. (Both universality and the fact that there is basically no overlap of the atomic wavefunctions closer than the vdW length clearly suggest that only pairwise interactions play a role in Efimov states.)
The question then came up (but was not really discussed) what exactly the role of short range interaction is in this context. Dipoles (aligned and in 2D) add an interesting spin to the mix: They produce an effective barrier, such that the smallest Efimov state is dominated by the dipolar length. It turns out (for this case as well as the one where dipoles are mixed with atoms) that the distance is always kept by having the particles in a kind of ring shape. The problem is, of course, that there are no molecules yet to do those experiments with, but Dy or similar might work.
The next question was whether long-range interactions (such as induced dipole moments in other particles) can have an effect. The names of Axilrod-Teller-Muto came up.

Q: Are there interesting quench dynamics? Is it possible to have non-local response due to non-local interaction, beyond ``light-cone" ?
Discussion: First, here it was necessary to clarify the expressions here. "Quench," in a many-body context, refers to any (sudden) change of a well-defined state that then results in decay or other phenomena. The pi/2-pulse in Kaden's talk on Thu is a very good example. "Light-cone" has nothing to do with the speed of light (which is, for all intents and purposes, assumed to be infinite), but refers to the propagation speed of excitations/correlations (Lieb-Robinson (sp?) bound - see also the paper that came up the discussion:
Light-cone-like spreading of correlations in a quantum many-body system, Nature 481, 484 (2012)). For zero-range interactions all correlations outside of the light-cone fall off exponentially, but in the case of dipole-dipole (or van-der-Waals) interactions this fall-off is polynomial. Insofar, the answer to the question above, is a very careful "yes." Edit:The answer is a definitive yes, in the sense that the Lieb-Robinson bounds allow for greater correlation outside of the light cone for systems with power-law interactions than for systems with short-range interactions. It has been shown rigorously (see Commun.Math.Phys. 265 (2006) 781-804 and Commun. Math. Phys., 265 (2006) 119-130) that "leakage" from the light cone is decaying exponentially for exponentially decaying interactions and is decaying as a power-law for power-law decaying interactions. Then there is the question on how this could be probed experimentally. This has been done in atoms (Bloch et al), but in molecules the question immediately comes up on how to detect molecules at all. (See next discussion point.)

Q: What many-body experiments with molecules do we expect do be realizable within the next five years?
Discussion: Quenching experiments might be considerably easier than experiments that simulate quantum phases because of the difficulty of preparing many-body ground-states with molecules. The question, however, is still dominated by how to detect molecules at all. So far, all "typical" detection schemes using laser fields suffer from way too weak coupling. What might be slightly easier is to ionize the molecules, which can be done (by estimate) so far to ~20%. Ions then can be detected with unit efficiency. The suggestion was to collect a list of the molecules that people use these days and ask the detection-scheme question (as well as the many-body experiment question) for the specific cases. The obvious candidates are KRb, KNa, as well as most other bi-alkalis, obviously OH and similar molecules due to their great elastic rates. Molecules which are real symmetric tops like NH_3 might be good choices, since they allow to completely and easily switch the dipole moments on and off. Some classes of "newer" molecules include YbRb, YbLi and other earth-alkali/alkali molecules, Sr_2 and similar for their lack of hf structure, molecular ions, what to do with Feshbach molecules?

Q: How many molecules make a CM system?
Discussion: Answer to the question: It depends. Tens of He atoms can make a superfluid state (exp). This is, however, probably an exception.
In order to see edge state physics (e.g., Majorana fermions) with dipole-dipole interactions, at least a 1D chain of 200 particles is needed (theo). (Can different, more efficient Hamiltonians be designed? .... no answer here) -- This whole question is highly model-dependent!
[How many particles have people been able to simulate?] Kagome lattice has been calculated with about 100 sites (periodic boundaries) to 700 sites (open boundaries) using DMRG (Phys. Rev. Lett. 109, 067201 (2012) see also Ann. Rev. of Cond. Mat. Phys., 3 111 (2012)). On the other hand, Ye's pancakes (with about 50 molecules/pancake) give already a nice experimental playground.
What might be interesting is studying the transition from a few particles into a "real" CM state.

Q. What are the most important decoherence mechanisms for molecules in fields?
Discussion: Since the first question was about the relative "badness" of optical lattices vs. control fields, this is where the discussion got stuck. So:
Q: How badly can optical lattices decohere molecules?
Discussion: It was determined that decoherence due to the presence of optical lattices is probably several (six?) orders of magnitude worse than for atoms. (The scattering goes with delta^(-2), where delta is the detuning of the standing wave laser field from the next-closest level. Due to the closeness of levels in molecule, this detuning cannot be very large.) Svetlana might go and calculate (Rayleigh and Raman) scattering rates for this question. In addition, there is blackbody radiation and possibly superradiance. Blackbody is relevant even for the 1K-range, and superradiance depends on the optical density (for those very long-wavelength transitions), which can be extremely high. In the infrared and visible parts of the spectrum molecules can be trapped in individual sites of the optical lattice. The depth of the lattice potential is determined by the real part of polarizability,
while the laser-induced decoherence is proportional to the imaginary part of the polarizability. For infrared and optical domains the dominant contribution to polarizability is from rovibrational levels of the excited electronic potentials rather than from the ground state potential. As calculation by S. Kotochigova and
E. Tiesinga [Phys.Rev.A 73, 041405(R) (2006)] shows that the imaginary part is proportional to the line width of the excited states and is smaller than the real part of the polarizability for both KRb and RbCs ground state molecules. In fact, the ratio between the real and imaginary parts of the polarizability is about 10^7 away from the resonances and significantly smaller (~10^3) near them. Optical potentials seen by KRb or RbCs molecules in these regions can be very deep (V_0/h ~ 1 MHz) for laser intensities on the order of 10^4 W/cm^2. At such intensities tunneling of molecules from one lattice site to another is negligible. Moreover, the decoherence time is significantly larger than 1 s.