| 研究課題/領域番号 |
18K13507
|
|---|
| 研究機関 | 沖縄科学技術大学院大学 |
|---|
研究代表者 |
FOGARTY Thomas 沖縄科学技術大学院大学, 量子システム研究ユニット, 研究員 (60786987)
|
|---|
| 研究期間 (年度) |
2018-04-01 – 2020-03-31
|
| キーワード | many-body supremacy / quantum heat engine / shortcut to adiabaticity / many-body optimisation / quantum phase transition |
|---|
| 研究実績の概要 |
In this financial year I have achieved many of the goals mentioned in my proposal and have made significant steps towards the completion of this project. In this time period I have published two papers directly related to the project at hand:
The first paper explored the dynamical properties of the Tonks-Girardeau (TG) gas during a sudden quench of an external lattice potential. This study examined how the different gapped and gapless energy spectrums inform the dynamics of the many-body state.
The second paper derived a shortcut to adiabaticity for 2 interacting particles. By using a variational approach I successfully showed that an efficient dynamical driving of interacting systems can be implemented using this technique.
Using the techniques learned from these two publications I have successfully calculated the performance of the many-body Otto cycle adiabatically and non-adiabatically. For the latter I implemented a variational many-body shortcut which improved the performance for short cycle times, even about the critical point, highlighting the feasibility of using a heat engine at a phase transition. The other main result is the presence of many-body supremacy in the engine. I show both analytically and numerically that the interacting many-body engine out-performs an ensemble of single particle non-interacting heat engines. This is particularly apparent when the interactions dominate over the lattice forces, and that the efficiency can be nearly tripled when more than 20 particles are used. At the moment I achieved most of the main results as stated in my proposal.
|
| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The project has progressed quite smoothly. There have already been 2 publications and a third is in preparation.
During the course of the project it was found that there are many interesting aspects to this type of system: non-trivial dynamics due to the phase of the system (super-fluid, insulating, super-solid) which have important considerations when implementing the engine cycle. This necessitated deriving a shortcut to adiabaticity for the many-body system. Using my knowledge of few-body dynamics I found that these techniques can be readily applied to larger systems.
The numerical simulations involved in this project are undertaken on OIST's Sango cluster, which allows for many parallel implementations of the code. This has allowed me to collect a lot of data encompassing a large parameter space which helps to succinctly describe the physical processes involved in the heat engine.
Analytically the adiabatic performance of the engine can be approximated in deep lattices. This allowed me to find compact equations which describe the many-body supremacy in the system. This nicely showed that when the interactions dominate there is a performance boost, however when interactions are suppressed the performance is reduced.
At the moment I achieved most of the main results of the critical many-body heat engine that I proposed, and a draft of the manuscript is in the later stages of preparation. I plan to submit this article to Physical Review Letters in June 2019.
|
| 今後の研究の推進方策 |
Further work will be be split into two sections:
1) Relation of many-body coherence to quantum dynamics and the quantum speed limit (QSL): The results from the first year of the project have lead me to investigate the role of coherence on out-of-equilibrium dynamics. Specifically, when engineering shortcuts to adiabaticity (STA) for many-body states how one quantifies the success of the STA can depend on the intended purpose of the quantum state. Going beyond the fidelity of the wavefunction, I have begun studying the reduced density matrix (RDM) of many-body systems, which describe quantum correlations and coherences. Comparing the dynamics of the TG gas and a non-interacting Fermi gas, the fidelity of the wavefunction is equivalent, but there are differences in the fidelity of the RDM due to the presence of large coherence in the TG gas. This suggests different QSLs for bosons and fermions even though the many-body fidelity is equivalent. This work would then extend the discussion on many-body thermodynamics to the QSL and the role of coherence.
2) Examine the effect of finite interactions on heat engine performance: This will be a non-trivial numerical challenge, but I hope to start with few-body systems (2 to 6 particles), which can be solved using current techniques at my disposal, before implementing larger systems. The presence of the energy gap will now depend on the interactions, which will modify the results, however many-body supremacy should still exist as long as a gap can be created.
|
| 次年度使用額が生じた理由 |
Travel costs were slightly below estimates, so remainder will be used in next fiscal year.
In the next financial year I will use funding to travel to Ireland to collaborate with colleagues in Trinity college Dublin. We will work on quantum speed limits in many-body systems and finish writing a manuscript on this topic. I will also attend the JPS Spring meeting and an international conference in the USA on atomic physics. I also plan to attend a workshop in Kyoto on quantum systems. The remainder of the funding will be publication costs for open access journals.
|
