scholarly journals Demystifying the spectral collapse in two-photon Rabi model

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Energy Spectrum ◽  
Bound States ◽  
Energy Levels ◽  
Scattering Problem ◽  
Critical Coupling ◽  
Discrete Energy ◽  
Two Photon ◽  
Continuous Energy ◽  
Rabi Model ◽  
Continuous Energy Spectrum

Abstract We have investigated the eigenenergy spectrum of the two-photon Rabi model at the critical coupling, particularly the special feature “spectral collapse”, by means of an elementary quantum mechanics approach. The eigenenergy spectrum is found to consist of both a set of discrete energy levels and a continuous energy spectrum. Each of these eigenenergies has a two-fold degeneracy corresponding to the spin degree of freedom. The discrete eigenenergy spectrum has a one-to-one mapping with that of a particle in a “Lorentzian function” potential well, and the continuous energy spectrum can be derived from the scattering problem associated with a potential barrier. The number of bound states available at the critical coupling is determined by the energy difference between the two atomic levels so that the extent of the “spectral collapse” can be monitored in a straightforward manner.

scholarly journals Spectral collapse in multiqubit two-photon Rabi model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Bound States ◽  
Energy Difference ◽  
Bound State ◽  
Potential Well ◽  
Critical Coupling ◽  
Nonlocal Potential ◽  
Two Photon ◽  
Rabi Model ◽  
Continuous Energy Spectrum ◽  
Bound State Problem

AbstractWe have shown that the smallest possible singel-qubit critical coupling strength of the N-qubit two-photon Rabi model is only 1/N times that of the two-photon Rabi model. The spectral collapse can thus occur at a more attainable value of the critical coupling. For both of the two-qubit and three-qubit cases, we have also rigorously demonstrated that at the critical coupling the system not only has a set of discrete eigenenergies but also a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in the presence of a finite potential well and a nonlocal potential. The energy difference of each qubit, which specifies both the depth of the finite potential well and the strength of the nonlocal potential, determines the number of bound states available, implying that the extent of the incomplete spectral collapse can be monitored in a straightforward manner.

scholarly journals Manipulating the spectral collapse in two-photon Rabi model

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Bound States ◽  
Photon Number ◽  
Energy Difference ◽  
Potential Well ◽  
Critical Coupling ◽  
Two Photon ◽  
Extra Term ◽  
Rabi Model ◽  
Continuous Energy Spectrum ◽  
Quadratic Coupling

Abstract We have investigated the eigenenergy spectrum of the two-photon Rabi model with a full quadratic coupling, particularly the special feature “spectral collapse”. The critical coupling strength is reduced by half from that of the two-photon Rabi model, implying that the spectral collapse can now occur at a more attainable value of the critical coupling. At the critical coupling some discrete eigenenergy levels still survive below the continuous energy spectrum, i.e. an incomplete spectral collapse, and the set of discrete eigenenergies has a one-to-one mapping with that of a particle of variable effective mass in a finite potential well. Since the energy difference between the two atomic levels specifies the depth of the potential well, the number of bound states available (or the extent of the “spectral collapse”) can be straightforwardly monitored. Obviously, this bears a great resemblance to the spectral collapse of the two-photon Rabi model, at least qualitatively. Moreover, since the full quadratic coupling includes an extra term proportional to the photon number operator only, our analysis indicates that one may manipulate the critical coupling of the two-photon Rabi model by incorporating an adjustable proportionality constant to this extra term.

scholarly journals Spectral collapse in anisotropic two-photon Rabi model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Bound States ◽  
Energy Levels ◽  
Energy Difference ◽  
Bound State ◽  
Discrete Energy ◽  
Radiation Mode ◽  
Two Photon ◽  
Rabi Model ◽  
Matter Interaction ◽  
Light Matter Interaction

AbstractIn this communication, based upon a squeezed-state trial wave function, we have performed a simple variational study of the spectral collapse in the anisotropic two-photon Rabi model. Our analysis indicates that the light-matter interaction and the spin-flipping (together with the anisotropy) effectively constitute two competing impacts upon the radiation mode. Whilst the former tries to decrease the radiation mode frequency, the latter may counteract or reinforce it. The light-matter interaction appears to dominate the frequency modulation as its coupling strengths go beyond the critical values, leading to the emergence of the spectral collapse. However, at the critical couplings the dominance of the light-matter interaction is not complete, and incomplete spectral collapse appears. Accordingly, at the critical couplings the eigenenergy spectrum comprises both a set of discrete energy levels and a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in a finite potential well, and the number of bound states available is determined by the energy difference between the two atomic levels. Each of these eigenenergies has a twofold degeneracy corresponding to the spin degree of freedom.

scholarly journals Revealing the Target Electronic Structure with Under-Threshold RABBIITT

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 66
Author(s):  
Anatoli Kheifets
Keyword(s):  
Electronic Structure ◽  
Bound States ◽  
Energy Levels ◽  
Laser Frequency ◽  
Target Atom ◽  
Oscillator Strengths ◽  
Ionization Threshold ◽  
Discrete Energy ◽  
Two Photon

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals the target atom electronic structure when one of the transitions proceeds from below the ionization threshold. Such an under-threshold RABBITT resonates with the target bound states and thus maps faithfully the discrete energy levels and the corresponding oscillator strengths. We demonstrate this sensitivity by considering the Ne atom driven by the combination of the XUV and IR pulses at the fundmanetal laser frequency in the 800 and 1000 nm ranges.

scholarly journals SPECTRAL AND TRANSPORT PROPERTIES OF ONE-DIMENSIONAL NANORING SUPERLATTICE

2013 ◽  
Vol 27 (20) ◽  
pp. 1350103 ◽  
Author(s):  
M. A. PYATAEV ◽  
M. A. KOKOREVA
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Electron Energy ◽  
Spectral Properties ◽  
Bound States ◽  
Energy Levels ◽  
Electron Energy Spectrum ◽  
Discrete Energy ◽  
One Dimensional ◽  
System Parameters

Spectral properties of periodic one-dimensional array of nanorings in a magnetic field are investigated. Two types of the superlattice are considered. In the first one, rings are connected by short one-dimensional wires while in the second one rings have immediate contacts between each other. The dependence of the electron energy on the quasimomentum is obtained from the Schrödinger equation for the Bloch wavefunction. We have found an interesting feature of the system, namely, presence of discrete energy levels in the spectrum. The levels can be located in the gaps or in the bands depending on parameters of the system. The levels correspond to bound states and electrons occupying these levels are located on individual rings or couples of neighboring rings and do not contribute to the charge transport. The wavefunction for the bound states corresponding to the discrete levels is obtained. Modification of electron energy spectrum with variation of system parameters is discussed.

scholarly journals Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields II

1997 ◽  
Vol 145 ◽  
pp. 69-98
Author(s):  
Tetsuya Hattori
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Discrete Spectrum ◽  
Bound States ◽  
Atomic System ◽  
Energy Levels ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Many Body ◽  
Discrete Energy

This paper is continuation from [10], in which we studied the discrete spectrum of atomic Hamiltonians with non-constant magnetic fields and, more precisely, we showed that any atomic system has only finitely many bound states, corresponding to the discrete energy levels, in a suitable magnetic field. In this paper we show another phenomenon in non-constant magnetic fields that any atomic system has infinitely many bound states in a suitable magnetic field.

Implantation profile of Na22 continuous energy spectrum positrons in silicon

2007 ◽  
Vol 101 (4) ◽  
pp. 043702 ◽  
Author(s):  
P. J. Foster ◽  
P. Mascher ◽  
A. P. Knights ◽  
P. G. Coleman
Keyword(s):  
Energy Spectrum ◽  
Continuous Energy ◽  
Continuous Energy Spectrum ◽  
Implantation Profile

scholarly journals DILATON DECAYS INTO UNPARTICLES AND A SINGLE PHOTON

2011 ◽  
Vol 26 (23) ◽  
pp. 3987-3996 ◽  
Author(s):  
G. A. KOZLOV ◽  
I. N. GORBUNOV
Keyword(s):  
Higgs Boson ◽  
Energy Spectrum ◽  
Rare Decays ◽  
Momentum Distribution ◽  
Radiative Decay ◽  
Single Photon ◽  
Missing Energy ◽  
Continuous Energy ◽  
Continuous Energy Spectrum ◽  
Energy And Momentum

We study the production of the vector U-unparticle stuff and a single photon in decays of a dilaton. The signals of an unparticle can be detected through the missing energy and momentum distribution carried away by U once it was produced in radiative decay of a dilaton. The continuous energy spectrum of the emitted photons encoding the recoil unparticle can be measured in precision studies of rare decays of the dilaton or Higgs-boson after their discoveries.

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