Few-fermion resonant tunneling and underbarrier trapping in asymmetric potentials
ELVIRA BILOKON , VALERIIA BILOKON , DUSTY LINDBERG , ANDRII SOTNIKOV , LEV KAPLAN , DENYS BONDAR
Tulane University, New Orleans, USA
Akhiezer Institute for Theoretical Physics, NSC KIPT, Kharkiv, Ukraine
Karazin Kharkiv National University, Kharkiv, Ukraine
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TUNNELING IS EVERYWHERE
Quantum cosmology
Fusion in low mass stars
Hawking radiation
Proton transfer
Alpha decay
Attosecond physics
SINGLE-PARTICLE TUNNELING
But, luckily, there are exceptions:�
Historically first: Asymmetric tunneling of interacting particles�[I. Amirkhanov and B. N. Zakhariev, Sov. Phys. JETP 22, 764 (1966)]
The same tunneling probability for the particle approaching the barrier from the left or the right
Landau L D and Lifshitz E M 1981 Quantum Mechanics:
Non-Relativistic Theory vol 3
See tutorial M. R. A. Shegelski and C. Sample, �Eur. J. Phys. 41, 035405 (2020)�
We mode BEC via the time-dependent Gross- Pitaevskii equation (GPE)
MODEL
FERMI-HUBBARD HAMILTONIAN:
MODEL
FERMI-HUBBARD HAMILTONIAN:
MODEL
FERMI-HUBBARD HAMILTONIAN:
MODEL
FERMI-HUBBARD HAMILTONIAN:
INITIAL STATE
The dynamics of the system can be described by the time-dependent Schrödinger equation
L=4-SITE SYSTEM
Two possible initial configurations
We calculate:
RESULTS
In the absence of the interaction, the tunneling is symmetric (this is proved analytically )
Barrier parameters
Noninteracting fermions
RESULTS
One particle is frozen
Falicov - Kimball limit
RESULTS
One particle is frozen
One particle is frozen
RESULTS
One particle is frozen
RESULTS
RESULTS
Falicov - Kimball limit
Frozening of one particle leads to the modification of the barrier
RESULTS
Symmetry consideration
For L=4 system, there are only two possible initial configurations
L = 6
Triplet state
RESULTS
Symmetry consideration
Singlet state
At , both and show noticeable growth.
RESULTS
L = 4, h =20J
RESULTS
Underbarrier resonant trapping
The trapping results from the conservation of total energy.
The initial state is a doublon positioned at the first site.
Energy conservation can be achieved not only by trapping the fermion at the site , but also by a doublon formation after the barrier.
RESULTS
Highly-asymmetric resonant tunneling
RESULTS
Highly-asymmetric resonant tunneling
RESULTS
Highly-asymmetric many-body resonant tunneling
This illustrates that the presence of the additional spin-up particle after the barrier does enhance the tunneling
Highly-asymmetric resonant tunneling
A doublon and a spin-up particle on opposite edges
of the one-dimensional lattice
A doublon from the left side of the barrier
CONCLUSIONS
THANK YOU!
RESULTS
Symmetry consideration
The action of the time evolution operator on the initial state:
Triplet state
Singlet state