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Diffraction of strongly interacting molecular Bose-Einstein condensate from standing wave light pulses
by Qi Liang, Chen Li, Sebastian Erne, Pradyumna Paranjape, RuGway Wu, Jörg Schmiedmayer
This is not the latest submitted version.
This Submission thread is now published as SciPost Phys. 12, 154 (2022)
|As Contributors:||Chen Li · Qi Liang · Pradyumna Paranjape · Jörg Schmiedmayer|
|Arxiv Link:||https://arxiv.org/abs/2201.01620v1 (pdf)|
|Date submitted:||2022-01-06 13:29|
|Submitted by:||Li, Chen|
|Submitted to:||SciPost Physics|
We study the effects of strong inter-particle interaction on diffraction of a Bose-Einstein condensate of $^6Li_2$ molecules from a periodic potential created by pulses of a far detuned optical standing wave. For short pulses we observe the standard Kapitza-Dirac diffraction, with the contrast of the diffraction pattern strongly reduced for very large interactions due to interaction dependent loss processes. For longer pulses diffraction shows the characteristic for matter waves impinging on an array of tubes and coherent channeling transport. We observe a slowing down of the time evolution governing the population of the momentum modes caused by the strong atom interaction. A simple physical explanation of that delay is the phase shift caused by the self interaction of the forming mater wave patters inside the standing light wave. The phenomenon can be reproduced with one-dimensional mean-field simulation. In addition two contributions to interaction-dependent degradation of the coherent diffraction patterns were identified: (i) in-trap loss of molecules during the lattice pulse, which involves dissociation of Feshbach molecules into free atoms, as confirmed by radio-frequency spectroscopy and (ii) collisions between different momentum modes during separation. This was confirmed by interferometrically recombining the diffracted momenta into the zero-momentum peak, which consequently removed the scattering background.
Submission & Refereeing History
Published as SciPost Phys. 12, 154 (2022)
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Reports on this Submission
Anonymous Report 2 on 2022-3-14 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2201.01620v1, delivered 2022-03-14, doi: 10.21468/SciPost.Report.4677
1- Novel experimental results
2- Strong interaction and long-pulse regimes explored
3- Theoretical modeling and interpretation of experimental observations
4- First experimental results on molecular BECs
1- Several effect like dissociation of Feshbach molecules and multiple scattering are essentially uncontrolled and complicate the analysis
2- Interpretation of simulation results and discussion of the discrepancies not entirely satisfactory
3- No attempt was undertaken to model the effects of multiple scattering or three-body recombination
This is an interesting work that pushes the widely used technique of diffracting matter waves from a standing light wave into new regimes by examining a molecular Bose-Einstein condensate and considering long pulses. It thus opens a new pathway in an existing research direction and should lead to follow-up work that would aim at better understanding the combined effects of molecular dissociation, three-body losses, and elastic scattering in molecular BECs.
I am not completely convinced by the discussion of interaction effects and comparison with Gross-Pitaevskii simulations. A slowing-down effect in the dynamics identified by the recurrence time of the zero momentum peak is identified in Gross-Pitaevskii simulations. In order to achieve qualitative agreement with experimental data, however, the rescaling parameter has to be multiplied with a fudge factor of value 4.2. It is argued that the mean-field simulations reproduce the experimentally observed effect and some qualitative justification of the fudge factor are presented. I do not find the arguments given entirely convincing and would lean to a different conclusion - namely that interaction effects are not satisfactorily captured by the 1D mean-field simulation.
The main argument given for the enhanced slowing down compared to mean-field simulations is the possibility of dissociated atoms being present in the BEC, while only molecules were assumed to be present for the simulation. As the molecule-molecule scattering length is 0.6a, where a is the atom-atom scattering length, and the atom-molecule scattering length is 1.2a, the presence of dissociated atoms may lead to increased mean-field interaction confounded by the fact that the number of interacting particles is also increased. Unfortunately, the presence of dissociated atoms, while confirmed in principle, could not be reliably quantified in the experiments.
I agree that the presence of dissociated atoms could increase effective mean field interactions, but would assume that such an effect would be quite moderate. I would expect an increase of the slowing parameter by less than a factor of 2, given that Fig. 6(b) seems to show something like a square root dependence of the slowing parameter on the interaction strength. I would rather interpret the bulk of the factor 4.2 increase of the slowing parameter as unexplained by the numerical mean-field simulation.
Loss of atom numbers is seen in experiments, but not quantitatively found in agreement with scattering calculations. Additional effects like three-body recombination and multiple scattering are believed to be present, and could in principle be modeled numerically as well. Have the authors considered at least estimating the quantitative effects of these processes?
1- The authors may want to consider mentioning in the abstract/conclusions that mean-field simulations and estimated effects of dissociated atoms cannot quantitatively explain the observed slowing-down effects of the dynamics.
2- Regarding the effects of multiple/secondary scattering events, the authors may want to consider estimating the expected effects, and refer to Thomas et al. Nat. Comms. 7, 12069 (2016) where such effects were quantified in experiments and simulation.
3- Fix typo "mater" in abstract.
4- Fix the first sentence of the second paragraph in Sec. 1 "The effect ...", as it's grammar appears to be broken.
5- The factor \eta should be defined in the caption of Fig. 6 for easier readability.
6- In the caption of Fig. 7 the difference between lines (2) and (3) is attributed to collision loss during TOF. Is this the only interpretation? Maybe a short discussion is warranted.
7- In the appendix A.3 on GPE simulations I would like to see, for completeness, more details that make it easier for others to reproduce the results:
7a- The formula used for g_1D should be given.
7b- The form of the external potential used (and relation to E_r) should be given (or a relevant reference cited).
7c- The chemical potential \mu shown in Fig. 11 should be defined in terms of the quantities of Eq. (1) (or should it appear in the equation?).
7d- Parameters of the simulation (how many lattice sites per computational box, discretisation parameters of the GPE) should be added.
Anonymous Report 1 on 2022-2-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2201.01620v1, delivered 2022-02-07, doi: 10.21468/SciPost.Report.4338
1- Novel experimental results in a simple, yet rich physics setting
2- Thorough theoretical analysis
3- Excellently written, very clear figures
4- Additional experiments (pulse sequences) were designed to answer open questions
1- Using a molecular BEC instead of a standard bosonic Feshbach-able species slightly complicates the interpretation of the measured results.
2- The measurements do not go beyond the mean-field regime.
The authors perform an in-depth experimental study of the effects of mean-field interactions on Kapitza-Dirac diffraction. The diffracting matter waves resulting from sudden flashes of an optical lattice consist of a molecular Bose-Einstein condensate of fermionic lithium-6. On the one hand, the authors study the transient, short-pulse regime. Except for a broadened background in time-of-flight, no major signatures of the interactions were observed. On the other hand, longer pulses (up to 1ms) lead to an interesting 'slowing' effect of the diffraction dynamics in addition to the previously observed incoherent background.
The slowing effect is qualitatively captured by Gross-Pitaevskii simulations. To my understanding, it results from the repulsive mean-field potential of the condensate counteracting the lattice potential and effectively reducing the lattice depth. The magnitude of the slowing effect is roughly a factor of four stronger than expected from the numerics and the authors provide possible reasons for this discrepancy.
The authors proceed to design experiments to investigate a possible cause of the incoherent background in time-of-flight expansion. A suitable lattice pulse sequence is designed to rephase all particles into the zero momentum peak, suggesting that the broad background occurs during the expansion. Overall, the authors provide convincing theoretical and experimental arguments as to why the incoherent background occurs.
To summarise, the authors provide novel experimental measurements of Kapitza-Dirac diffraction in the interacting regime, which has largely remained unexplored to date. Therefore, I would recommend publication in SciPost Physics.
1- The authors provide a nice qualitative explanation for the slowing effect (section 4.1 on page 7), as reduction of lattice depth due to a repulsive mean-field potential. The argument could be made even more explicit by calculating an effective reduction of lattice depth in recoil energies. This could be achieved by fitting the diffraction dynamics to the noninteracting numerics, leaving the lattice depth as a free parameter. Then the y-axis in Fig.6b could be expressed as 'cancelling lattice depth' (if the relation is linear in this regime).
2- A few technical details on the optical lattice are missing: How is the lattice depth calibrated? What is the estimated phase stability of the lattice? Could a jittering optical lattice (due to an unstable phase) contribute to the interaction-dependent incoherent background observed in the experiment?
3- As far as I understood, the numerics are scaled on the x-axis to match the experimental data, taking the slowing parameter r as a free parameter. Throughout the plots in the manuscript, the authors should clarify which theory curves are without free parameters and which curves are fits to the data (especially in Fig. 4 on the right, in which the theory agrees very well with the data - is this a fit or an a priori theory curve without free parameters?).
4- What is expected to happen in the beyond-mean-field regime?
5- The effects of mean-field interactions on rapid triangular optical lattice ramps were previously studied in "Observing Localization in a 2D Quasicrystalline Optical Lattice" by Sbroscia et al. PRL 125, 200604 (2020). Can the authors comment on the relation to their results?
- Why is the lattice depth changed from 500Er to 50Er between sections 3 and 4? The authors should explain this briefly.
- a typo at the bottom of page 3: "afterwords"
- Fig 4 (right): the x-label "1000" does not match the tick of 1000us.
- Fig 4: the slowing is not evident from the dashed line as it is. Stronger tick markings (and more ticks) or a grid could help, or maybe a zoom on the relevant region with the dashed line (such as Fig. 6a).
- In general, the ticks in all figures except Fig6b are too thin.