Chandra Adhikari - Academia.edu (original) (raw)
Thesis Chapters by Chandra Adhikari
We have performed first-principles calculations to study the electronic structures and magnetic p... more We have performed first-principles calculations to study the electronic structures and magnetic properties of (i) three transition metals: Mn Pd and Pt (ii)two ordered alloys: Pt3 Mn and Pd3 Mn and (iii)two disordered alloys: Pt_{1−x} Mn_x (x=0.50, 0.25, 0.20) and Pd_{1−x}Mn_x(x=0.10, 0.05, 0.01). The first-principles calculations have been implemented by TB-LMTO-ASA for transition metals and ordered alloys and TB-LMTO-ASR for disordered alloys. We have estimated the magnetic moments of transition metals and individual transition metals in alloys and compare with available experimental data. We have further studied the stability of non-collinear spin arrangements(1Q, 2Q, 3Q) in Pd_{75}Mn_{25}. Findings show that 1Q is the most stable spin structure in Pd_{75}Mn_{25}.
Papers by Chandra Adhikari
We study the long-range interaction between two hydrogen atoms, in both the van der Waals and Cas... more We study the long-range interaction between two hydrogen atoms, in both the van der Waals and Casimir-Polder regimes. The retardation regime is reached when the finiteness of the speed of light becomes relevant. Provided that both atoms are in the ground states, the retardation regime is achieved when the interatomic distance, R, is larger than 137 a 0 , where a 0 is the Bohr radius. v
International Journal of Operational Research Nepal, Dec 31, 2023
Authorea (Authorea), Mar 6, 2023
Springer eBooks, 2018
We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function ... more We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of "hidden" symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higher-dimensional irreducible matrices is indicated, and an application to the 2S-2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.
Bulletin of the American Physical Society, May 31, 2018
Submitted for the DAMOP18 Meeting of The American Physical Society Long-Range Tails in van der Wa... more Submitted for the DAMOP18 Meeting of The American Physical Society Long-Range Tails in van der Waals Interactions 1 ULRICH JENTSCHURA, CHANDRA ADHIKARI, VINCENT DEBIERRE, Missouri Univ of Sci Tech-We investigate the oscillatory long-range tails of long-range interatomic interactions, based on a quantum electrodynamic formalism. The matching of the scattering amplitude to the effective Hamiltonian conclusively answers any questions regarding the placement of the so-called pole terms, which correspond to a very particular physical process, namely, virtual resonant emission into an energetically lower atomic state. The resonant process leads to conceptually interesting, but numerically small, oscillatory long-range tails. These tails drastically differ from the predictions of Casimir-Polder theory [Phys. Rev. Lett. 118, 123001 (2017)]. Phenomenologically, it is interesting to note that for the first time, we are now in the position to also calculate the short-range, non-retarded, van der Waals effects for systems involving excited (Rydberg) atoms. The van der Waals coefficients, in atomic units, are found to be in the range of a few 100,000. The calculations enable us to estimate the pressure shift of such transitions, which are crucial for the determination of fundamental constants from current, and planned, high-precision measurements involving simple atomic systems.
Journal of Physics B, Mar 19, 2019
We investigate collisional shifts of spectral lines involving excited hydrogenic states, where va... more We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.
Physical review, Sep 20, 2016
Recently, we have studied the magic wavelength for the atomic hydrogen 1S-2S transition [A.K., Ph... more Recently, we have studied the magic wavelength for the atomic hydrogen 1S-2S transition [A.K., Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this addendum, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. At the magic wavelength, the lowest-order ac Stark shifts of the 1S and 2S states are equal; it is found to be equal to 514.6 nm. The ac Stark shift at the magic wavelength is −221.6 Hz/(kW/cm 2), and the slope of the ac Stark shift at the magic wavelength under a change of the driving laser frequency is −0.215 7 Hz/(GHz kW/cm 2).
Journal of Physics B, Mar 19, 2019
We study the theoretical foundations for the pressure shifts in highprecision atomic beam spectro... more We study the theoretical foundations for the pressure shifts in highprecision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P 1/2 and 4P 3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P-2S interaction, where the inclusion of quasidegenerate 4S-2P 1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasidegenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R 6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atommolecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.
Physical review, Feb 2, 2017
The theory of the long-range interaction of metastable excited atomic states with ground-state at... more The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6(2S; 1S) describing the interaction of metastable atomic hydrogen (2S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0/α, where a0 = /(αmc) is the Bohr radius and α is the fine structure constant, one finds the symmetry-dependent result E2S;1S(R) ≈ (−176.75 ± 27.98) E h (a0/R) 6 (E h denotes the Hartree energy). In the Casimir-Polder range a0/α ≪ R ≪ c/L, where L ≡ E 2S 1/2 − E 2P 1/2 is the Lamb shift energy, one finds E2S;1S(R) ≈ (−121.50 ± 46.61) E h (a0/R) 6. In the the Lamb shift range R ≫ c/L, we find an oscillatory tail with a negligible interaction energy below 10 −36 Hz. Dirac-δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction, or, expressed differently, the shift of the hydrogen 2S hyperfine frequency due to interactions with neighboring 1S atoms. The 2S hyperfine frequency has recently been measured very accurately in atomic beam experiments.
Physical review, Jul 12, 2022
The optical properties of monocrystalline, intrinsic silicon are of interest for technological ap... more The optical properties of monocrystalline, intrinsic silicon are of interest for technological applications as well as fundamental studies of atom-surface interactions. For an enhanced understanding, it is of great interest to explore analytic models which are able to fit the experimentally determined dielectric function ǫ(T∆, ω), over a wide range of frequencies and a wide range of the temperature parameter T∆ = (T − T0)/T0, where T0 = 293 K represents room temperature. Here, we find that a convenient functional form for the fitting of the dielectric function of silicon involves a Lorentz-Dirac curve with a complex, frequency dependent amplitude parameter which describes radiation reaction. We apply this functional form to the expression [ǫ(T∆, ω) − 1]/[ǫ(T∆, ω) + 2], inspired by the Clausius-Mossotti relation. With a very limited set of fitting parameters, we are able to represent, to excellent accuracy, experimental data in the (angular) frequency range 0 < ω < 0.16 a.u. and 0 < T∆ < 2.83, corresponding to the temperature range 293 K < T < 1123 K. Using our approach, we evaluate the short-range C3 and the long-range C4 coefficients for the interaction of helium atoms with the silicon surface. In order to validate our results, we compare to a separate temperature-dependent direct fit of ǫ(T∆, ω) to the Lorentz-Dirac model.
Bulletin of the American Physical Society, Apr 15, 2018
We analyze the long-range interactions between two hydrogen atoms. Provided both atoms are in the... more We analyze the long-range interactions between two hydrogen atoms. Provided both atoms are in the ground states, the retardation regime is achieved when the interatomic distance, R, is larger than 137a 0 , where a 0 is the Bohr radius. However, for an excited atom interacting with the ground state atom, the presence of virtually low lying energy levels accessible by a dipole transition from an excited reference state makes the situation different. For excited reference states, we match the scattering amplitude and effective perturbation Hamiltonian of the system. For a 0 ≪ R ≪ 137a 0 , the nonretarded approximation is valid and the interaction energy takes a R −6 functional form. For a higher excited states, we obtain a numerically large van der Waals coefficient, e.g., about 24000 in atomic units for 12S-1S system. As soon as the interatomic separation satisfies R ≥ 137a 0 , the interaction energy does not have only the R −6 term, but surprisingly it also has (i) attractive/repulsive oscillatory terms, in addition to (ii) the familiar Casimir-Polder R −7 asymptotic. For sufficiently large R, the oscillatory term whose magnitude falls off as R −2 dominates the Wick-rotated term (the latter describes the retarded Casimir-Polder type of interaction).
Physical Review Letters, Sep 1, 2016
Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S transition [A. Kawasaki, ... more Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S transition [A. Kawasaki, Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this paper, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. The magic wavelength, at which the lowest-order ac Stark shifts of the 1S and 2S states are equal, is found to be 514.6 nm. The ac Stark shift at the magic wavelength is −221.6 Hz/(kW/cm 2), and the slope of the ac Stark shift at the magic wavelength under a change of the driving laser frequency is −0.2157 Hz/[GHz (kW/cm 2)].
Physical Review Letters, Mar 20, 2017
We report on a quantum electrodynamic (QED) investigation of the interaction between a ground sta... more We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails which are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term which depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the ungerade state for close approach), and we include all nonresonant states in our rigorous QED treatment. In order to illustrate the findings, we analyze the fine-structure resolved van der Waals interaction for nD-1S hydrogen interactions with n = 8, 10, 12 and find surprisingly large numerical coefficients.
Journal of Physics B, Oct 16, 2018
The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir... more The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir-Polder interaction using time-ordered perturbation theory, to the matching of the scattering amplitude using quantum electrodynamics. In the first case, a total of twelve time-ordered diagrams need to be considered, while in the second case, one encounters only two Feynman diagrams, namely, the ladder and crossed-ladder contributions. For ground-state interactions, we match the contribution of six of the time-ordered diagrams against the corresponding Feynman diagrams, showing the consistency of the two approaches. Second, we also examine the leading radiative correction to the long-range interaction, which is of relative order O(α 3). In doing so, we uncover logarithmic terms, in both the interatomic distance as well as the fine-structure constant, in higher-order corrections to the Casimir-Polder interaction.
Physical review, Sep 5, 2017
The long-range interaction of excited neutral atoms has a number of interesting and surprising pr... more The long-range interaction of excited neutral atoms has a number of interesting and surprising properties, such as the prevalence of long-range, oscillatory tails, and the emergence of numerically large van der Waals C6 coefficients. Furthermore, the energetically quasi-degenerate nP states require special attention and lead to mathematical subtleties. Here, we analyze the interaction of excited hydrogen atoms in nS states (3 ≤ n ≤ 12) with ground-state hydrogen atoms, and find that the C6 coefficients roughly grow with the fourth power of the principal quantum number, and can reach values in excess of 240 000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R ≪ a0/α, where a0 is the Bohr radius and α is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a0/α ≪ R ≪ c/L, where L is the Lamb shift energy. In this range, the contribution of quasi-degenerate excited nP states remains nonretarded and competes with the 1/R 2 and 1/R 4 tails of the pole terms which are generated by lower-lying mP states with 2 ≤ m ≤ n − 1, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range R ≫ c/L. The familiar 1/R 7 asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation, for highly excited states.
![Research paper thumbnail of Publisher's Note: Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved 2S−2S systems [Phys. Rev. A 95, 022704 (2017)]](https://attachments.academia-assets.com/109035370/thumbnails/1.jpg)
](Physical Review A, 2017
The title should read as "Long-range interactions of hydrogen atoms in excited states. II. Hyperf... more The title should read as "Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved 2S-2S systems." On page 1, left-hand column, the third line of the first paragraph should read as "out an analysis of the hyperfine-resolved 2S-2S system... ." The title and text have been corrected as of 9 February 2017. The title and text are correct in the printed version of the journal.
Condensed Matter
We present a theoretical study on the energy dispersion of an ultrathin film of periodically-alig... more We present a theoretical study on the energy dispersion of an ultrathin film of periodically-aligned single-walled carbon nanotubes (SWCNTs) with the help of the Bogoliubov–Valatin transformation. The Hamiltonian of the film was derived using the many-particle green function technique in the Matsubara frequency formalism. The periodic array of SWCNTs was embedded in a dielectric with comparatively higher permittivity than the substrate and the superstrate such that the SWCNT film became independent with the axis of quantization but keeps the thickness as the variable parameter, making the film neither two-dimensional nor three-dimensional, but transdimensional. It was revealed that the energy dispersion of the SWCNT film is thickness dependent.
Atoms
We calculate the fully retarded one-photon exchange interaction potential between electrically ne... more We calculate the fully retarded one-photon exchange interaction potential between electrically neutral, identical atoms, one of which is assumed to be in an excited state, by matching the scattering matrix (S matrix) element with the effective Hamiltonian. Based on the Feynman prescription, we obtain the imaginary part of the interaction energy. Our results lead to precise formulas for the distance-dependent enhancement and suppression of the decay rates of entangled superradiant and subradiant Dicke states (Bell states), as a function of the interatomic distance. The formulas include a long-range tail due to entanglement. We apply the result to an example calculation involving two hydrogen atoms, one of which is in an excited P state.
Advanced Optical Materials
We have performed first-principles calculations to study the electronic structures and magnetic p... more We have performed first-principles calculations to study the electronic structures and magnetic properties of (i) three transition metals: Mn Pd and Pt (ii)two ordered alloys: Pt3 Mn and Pd3 Mn and (iii)two disordered alloys: Pt_{1−x} Mn_x (x=0.50, 0.25, 0.20) and Pd_{1−x}Mn_x(x=0.10, 0.05, 0.01). The first-principles calculations have been implemented by TB-LMTO-ASA for transition metals and ordered alloys and TB-LMTO-ASR for disordered alloys. We have estimated the magnetic moments of transition metals and individual transition metals in alloys and compare with available experimental data. We have further studied the stability of non-collinear spin arrangements(1Q, 2Q, 3Q) in Pd_{75}Mn_{25}. Findings show that 1Q is the most stable spin structure in Pd_{75}Mn_{25}.
We study the long-range interaction between two hydrogen atoms, in both the van der Waals and Cas... more We study the long-range interaction between two hydrogen atoms, in both the van der Waals and Casimir-Polder regimes. The retardation regime is reached when the finiteness of the speed of light becomes relevant. Provided that both atoms are in the ground states, the retardation regime is achieved when the interatomic distance, R, is larger than 137 a 0 , where a 0 is the Bohr radius. v
International Journal of Operational Research Nepal, Dec 31, 2023
Authorea (Authorea), Mar 6, 2023
Springer eBooks, 2018
We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function ... more We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of "hidden" symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higher-dimensional irreducible matrices is indicated, and an application to the 2S-2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.
Bulletin of the American Physical Society, May 31, 2018
Submitted for the DAMOP18 Meeting of The American Physical Society Long-Range Tails in van der Wa... more Submitted for the DAMOP18 Meeting of The American Physical Society Long-Range Tails in van der Waals Interactions 1 ULRICH JENTSCHURA, CHANDRA ADHIKARI, VINCENT DEBIERRE, Missouri Univ of Sci Tech-We investigate the oscillatory long-range tails of long-range interatomic interactions, based on a quantum electrodynamic formalism. The matching of the scattering amplitude to the effective Hamiltonian conclusively answers any questions regarding the placement of the so-called pole terms, which correspond to a very particular physical process, namely, virtual resonant emission into an energetically lower atomic state. The resonant process leads to conceptually interesting, but numerically small, oscillatory long-range tails. These tails drastically differ from the predictions of Casimir-Polder theory [Phys. Rev. Lett. 118, 123001 (2017)]. Phenomenologically, it is interesting to note that for the first time, we are now in the position to also calculate the short-range, non-retarded, van der Waals effects for systems involving excited (Rydberg) atoms. The van der Waals coefficients, in atomic units, are found to be in the range of a few 100,000. The calculations enable us to estimate the pressure shift of such transitions, which are crucial for the determination of fundamental constants from current, and planned, high-precision measurements involving simple atomic systems.
Journal of Physics B, Mar 19, 2019
We investigate collisional shifts of spectral lines involving excited hydrogenic states, where va... more We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.
Physical review, Sep 20, 2016
Recently, we have studied the magic wavelength for the atomic hydrogen 1S-2S transition [A.K., Ph... more Recently, we have studied the magic wavelength for the atomic hydrogen 1S-2S transition [A.K., Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this addendum, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. At the magic wavelength, the lowest-order ac Stark shifts of the 1S and 2S states are equal; it is found to be equal to 514.6 nm. The ac Stark shift at the magic wavelength is −221.6 Hz/(kW/cm 2), and the slope of the ac Stark shift at the magic wavelength under a change of the driving laser frequency is −0.215 7 Hz/(GHz kW/cm 2).
Journal of Physics B, Mar 19, 2019
We study the theoretical foundations for the pressure shifts in highprecision atomic beam spectro... more We study the theoretical foundations for the pressure shifts in highprecision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P 1/2 and 4P 3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P-2S interaction, where the inclusion of quasidegenerate 4S-2P 1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasidegenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R 6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atommolecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.
Physical review, Feb 2, 2017
The theory of the long-range interaction of metastable excited atomic states with ground-state at... more The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6(2S; 1S) describing the interaction of metastable atomic hydrogen (2S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0/α, where a0 = /(αmc) is the Bohr radius and α is the fine structure constant, one finds the symmetry-dependent result E2S;1S(R) ≈ (−176.75 ± 27.98) E h (a0/R) 6 (E h denotes the Hartree energy). In the Casimir-Polder range a0/α ≪ R ≪ c/L, where L ≡ E 2S 1/2 − E 2P 1/2 is the Lamb shift energy, one finds E2S;1S(R) ≈ (−121.50 ± 46.61) E h (a0/R) 6. In the the Lamb shift range R ≫ c/L, we find an oscillatory tail with a negligible interaction energy below 10 −36 Hz. Dirac-δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction, or, expressed differently, the shift of the hydrogen 2S hyperfine frequency due to interactions with neighboring 1S atoms. The 2S hyperfine frequency has recently been measured very accurately in atomic beam experiments.
Physical review, Jul 12, 2022
The optical properties of monocrystalline, intrinsic silicon are of interest for technological ap... more The optical properties of monocrystalline, intrinsic silicon are of interest for technological applications as well as fundamental studies of atom-surface interactions. For an enhanced understanding, it is of great interest to explore analytic models which are able to fit the experimentally determined dielectric function ǫ(T∆, ω), over a wide range of frequencies and a wide range of the temperature parameter T∆ = (T − T0)/T0, where T0 = 293 K represents room temperature. Here, we find that a convenient functional form for the fitting of the dielectric function of silicon involves a Lorentz-Dirac curve with a complex, frequency dependent amplitude parameter which describes radiation reaction. We apply this functional form to the expression [ǫ(T∆, ω) − 1]/[ǫ(T∆, ω) + 2], inspired by the Clausius-Mossotti relation. With a very limited set of fitting parameters, we are able to represent, to excellent accuracy, experimental data in the (angular) frequency range 0 < ω < 0.16 a.u. and 0 < T∆ < 2.83, corresponding to the temperature range 293 K < T < 1123 K. Using our approach, we evaluate the short-range C3 and the long-range C4 coefficients for the interaction of helium atoms with the silicon surface. In order to validate our results, we compare to a separate temperature-dependent direct fit of ǫ(T∆, ω) to the Lorentz-Dirac model.
Bulletin of the American Physical Society, Apr 15, 2018
We analyze the long-range interactions between two hydrogen atoms. Provided both atoms are in the... more We analyze the long-range interactions between two hydrogen atoms. Provided both atoms are in the ground states, the retardation regime is achieved when the interatomic distance, R, is larger than 137a 0 , where a 0 is the Bohr radius. However, for an excited atom interacting with the ground state atom, the presence of virtually low lying energy levels accessible by a dipole transition from an excited reference state makes the situation different. For excited reference states, we match the scattering amplitude and effective perturbation Hamiltonian of the system. For a 0 ≪ R ≪ 137a 0 , the nonretarded approximation is valid and the interaction energy takes a R −6 functional form. For a higher excited states, we obtain a numerically large van der Waals coefficient, e.g., about 24000 in atomic units for 12S-1S system. As soon as the interatomic separation satisfies R ≥ 137a 0 , the interaction energy does not have only the R −6 term, but surprisingly it also has (i) attractive/repulsive oscillatory terms, in addition to (ii) the familiar Casimir-Polder R −7 asymptotic. For sufficiently large R, the oscillatory term whose magnitude falls off as R −2 dominates the Wick-rotated term (the latter describes the retarded Casimir-Polder type of interaction).
Physical Review Letters, Sep 1, 2016
Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S transition [A. Kawasaki, ... more Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S transition [A. Kawasaki, Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this paper, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. The magic wavelength, at which the lowest-order ac Stark shifts of the 1S and 2S states are equal, is found to be 514.6 nm. The ac Stark shift at the magic wavelength is −221.6 Hz/(kW/cm 2), and the slope of the ac Stark shift at the magic wavelength under a change of the driving laser frequency is −0.2157 Hz/[GHz (kW/cm 2)].
Physical Review Letters, Mar 20, 2017
We report on a quantum electrodynamic (QED) investigation of the interaction between a ground sta... more We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails which are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term which depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the ungerade state for close approach), and we include all nonresonant states in our rigorous QED treatment. In order to illustrate the findings, we analyze the fine-structure resolved van der Waals interaction for nD-1S hydrogen interactions with n = 8, 10, 12 and find surprisingly large numerical coefficients.
Journal of Physics B, Oct 16, 2018
The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir... more The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir-Polder interaction using time-ordered perturbation theory, to the matching of the scattering amplitude using quantum electrodynamics. In the first case, a total of twelve time-ordered diagrams need to be considered, while in the second case, one encounters only two Feynman diagrams, namely, the ladder and crossed-ladder contributions. For ground-state interactions, we match the contribution of six of the time-ordered diagrams against the corresponding Feynman diagrams, showing the consistency of the two approaches. Second, we also examine the leading radiative correction to the long-range interaction, which is of relative order O(α 3). In doing so, we uncover logarithmic terms, in both the interatomic distance as well as the fine-structure constant, in higher-order corrections to the Casimir-Polder interaction.
Physical review, Sep 5, 2017
The long-range interaction of excited neutral atoms has a number of interesting and surprising pr... more The long-range interaction of excited neutral atoms has a number of interesting and surprising properties, such as the prevalence of long-range, oscillatory tails, and the emergence of numerically large van der Waals C6 coefficients. Furthermore, the energetically quasi-degenerate nP states require special attention and lead to mathematical subtleties. Here, we analyze the interaction of excited hydrogen atoms in nS states (3 ≤ n ≤ 12) with ground-state hydrogen atoms, and find that the C6 coefficients roughly grow with the fourth power of the principal quantum number, and can reach values in excess of 240 000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R ≪ a0/α, where a0 is the Bohr radius and α is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a0/α ≪ R ≪ c/L, where L is the Lamb shift energy. In this range, the contribution of quasi-degenerate excited nP states remains nonretarded and competes with the 1/R 2 and 1/R 4 tails of the pole terms which are generated by lower-lying mP states with 2 ≤ m ≤ n − 1, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range R ≫ c/L. The familiar 1/R 7 asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation, for highly excited states.
Physical Review A, 2017
The title should read as "Long-range interactions of hydrogen atoms in excited states. II. Hyperf... more The title should read as "Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved 2S-2S systems." On page 1, left-hand column, the third line of the first paragraph should read as "out an analysis of the hyperfine-resolved 2S-2S system... ." The title and text have been corrected as of 9 February 2017. The title and text are correct in the printed version of the journal.
Condensed Matter
We present a theoretical study on the energy dispersion of an ultrathin film of periodically-alig... more We present a theoretical study on the energy dispersion of an ultrathin film of periodically-aligned single-walled carbon nanotubes (SWCNTs) with the help of the Bogoliubov–Valatin transformation. The Hamiltonian of the film was derived using the many-particle green function technique in the Matsubara frequency formalism. The periodic array of SWCNTs was embedded in a dielectric with comparatively higher permittivity than the substrate and the superstrate such that the SWCNT film became independent with the axis of quantization but keeps the thickness as the variable parameter, making the film neither two-dimensional nor three-dimensional, but transdimensional. It was revealed that the energy dispersion of the SWCNT film is thickness dependent.
Atoms
We calculate the fully retarded one-photon exchange interaction potential between electrically ne... more We calculate the fully retarded one-photon exchange interaction potential between electrically neutral, identical atoms, one of which is assumed to be in an excited state, by matching the scattering matrix (S matrix) element with the effective Hamiltonian. Based on the Feynman prescription, we obtain the imaginary part of the interaction energy. Our results lead to precise formulas for the distance-dependent enhancement and suppression of the decay rates of entangled superradiant and subradiant Dicke states (Bell states), as a function of the interatomic distance. The formulas include a long-range tail due to entanglement. We apply the result to an example calculation involving two hydrogen atoms, one of which is in an excited P state.
Advanced Optical Materials
Applied Physics B, 2016
We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function ... more We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of "hidden" symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higher-dimensional irreducible matrices is indicated, and an application to the 2S-2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.