2021 Fiscal Year Research-status Report
Exploring the effect of correlations on quantum speed limits in interacting cold atom systems
| Project/Area Number |
21K13856
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| Research Institution | Okinawa Institute of Science and Technology Graduate University |
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Principal Investigator |
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, スタッフサイエンティスト (60786987)
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| Project Period (FY) |
2021-04-01 – 2023-03-31
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| Keywords | quantum speed limits / orthogonality / interacting states / quantum control / quantum entanglement / supersymmetry |
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| Outline of Annual Research Achievements |
In the past year work has progressed significantly on exploring non-equilibrium dynamics and quantum speed limits in interacting cold atom systems. This includes 3 publications (2 in Physical Review Letters and 1 in Quantum) along with 2 preprints. A highlight of these published works was a PRL exploring the effects of interactions on information scrambling and non-equilibrium work statistics. We showed that the presence of interactions is essential for meaningful scrambling on short time scales and that it is proportional to the variance of the work distribution. Indeed, the variance bounds the speed of state evolution, with intermediate interactions non-trivially modifying the energy spectrum and therefore increasing the energetic excitations, allowing for faster scrambling. The published work in Quantum also explores how energy level statistics affects dynamics, suggesting that this may also impact the QSL.
As of compiling this report a manuscript is near completion on quantum speed limits using supersymmetric Hamiltonians. In this work we have used the algebra of supersymmetry to describe both the non-equilibrium and controlled dynamics of particles confined to a hierarchy of supersymmetric Hamiltonians. The novelty here lies in the exact mapping between different potentials which can be used to characterize a class of quantum speed limits which are related through their shared super-potential. We also show that the energetic cost of performing a shortcut to adiabaticity is the same for all groundstates in any supersymmetric potential of the chosen hierarchy.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Preliminary work on non-equilibrium dynamics was undertaken and is progressing at a good pace. The scrambling paper highlights the effects of interactions on the dynamics of small systems and this relation to thermodynamics quantities (variance) and information (fidelity and squared commutator). Of course these are important quantities when exploring quantum speed limits (QLSs), and now that the system is understood a more focussed effort will be forthcoming to explore QSLs for different metrics in few body systems. For instance, comparing the QSLs of the full pure state with that of the reduced single particle density matrix which is inherently mixed when interactions are present. My work on quantum chaos in interacting systems (Quantum 2021) also suggests an important role of the energy spacing statistics on QSLs that will be further explored.
The project was also expanded to explore the role of supersymmetry on quantum speed limits. This was undertaken as the supersymmetric algebra allows to connect a hierarchy of Hamiltonians through a shared super-potential. Here the energy spectra are essentially equivalent for any potential, implying that the quantum speed limit should also be unchanged. These systems are also highly analytic in nature allowing for exact expressions for the QSLs of single particle systems. A pre-print has been written which explores quench dynamics in many-body Fermi gases in super-symmetric potentials and a follow up work exploring QSLs in these potentials is currently near completion.
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| Strategy for Future Research Activity |
Future work will encompass two main works:
Firstly, completing the paper on QSLs in supersymmetric single particle dynamics. The numerical calculations are complete and the remaining work focusses on finishing the manuscript. The main result is analytic expressions for the energetic cost and QSL for range of different potentials in the supersymmetric hierarchy of the infinite square well, which are related due to intertwining properties between the different time-dependent Hamiltonians. Follow up work would explore interacting two-body states in these potentials, where the interaction significantly alters the super-symmetric potential, possibly leading to non-local terms in the Hamiltonian.
Secondly, the draft of the QSLs in interacting few-body systems needs to be written. Most of the calculations are complete, for instance, the Mandelstam-Tamm bound for trap quenches of 2-4 interacting particles. Similar to information scrambling, intermediate interactions can reduce the quantum speed limit time significantly due to the non-trivial energy spectrum. Interesting comparisons can also be made between scale invariant quenches - where the quenched state can be written as a re-scaled solution of the initial Hamiltonian. Here the energy spectrum possesses the same energy spacing statistics as the initial Hamiltonian, which is similar conceptually to the supersymmetric potentials. In this case this also results in a tighter speed limit. This work will be extended to look at the reduced single particle dynamics, which includes coherences and correlations.
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| Causes of Carryover |
Due to covid many conferences were held online, also due to re-entry restrictions to Japan it was not possible to attend international conferences or visit other research groups. With the opening of international borders and easing of travel restrictions I plan to use this budget in the current financial year for international conferences and business trips.
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