Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Chemical Education

Analog computation for the quantized simple harmonic oscillator

R. Wayne Ohline

Published Feb 1, 1974• 0 citations
Publisher

Abstract

The authors have constructed a computer for the quantized simple harmonic oscillator which has performed quite satisfactorily using inexpensive integrated circuit components.
DOI
10.1021/ed051p144.1

Related papers

Quantization of Simple Harmonic Oscillator

Hiu Yung Wong

Springer eBooks•Jan 1, 2025•0 citations

On quantization of simple harmonic oscillators

Kazuhiko Odaka, Tatsuya Kishi, S. Kamefuchi

A general framework is presented of quantizing the system of a simple harmonic oscillator. Various methods of quantization so far proposed are accommodated here in a unified form. Some remarks are also made on quantization for the case of more than one oscillator.

Journal of Physics A Mathematical and General•Jun 7, 1991•85 citations

Physical Realization of Harmonic Oscillator Quantum Computer

Jun Lu

Lecture notes in electrical engineering•Jan 1, 2012•1 citation

Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses

Z. Ficek, S. Swain

We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the Rabi frequency ${\ensuremath{\Omega}}_{c}$ of the cavity field to that of the Rabi frequency $\ensuremath{\Omega}$ of the driving field. For ${\ensuremath{\Omega}}_{c}<\ensuremath{\Omega}$ and moderate coupling of the transition to the cavity mode the spectral peaks are composed of multiplets. A quantized dressed-atom approach provides a simple explanation of the spectral features and shows that the oscillations in the spectral components arise from the oscillations of the population distribution in the dressed states. The observation of these features would provide evidence for the quantum nature of the cavity field. The distribution is an analog of the harmonic-oscillator probability distribution function, and should be experimentally observable. For ${\ensuremath{\Omega}}_{c}>~\ensuremath{\Omega}$ there is no Autler-Townes splitting and the spectrum is composed of a single peak located at the frequency of the probe transition. We show that this effect results from the collapse of the atom to the ground state, which has been predicted by Alsing, Cardimona, and Carmichael [Phys. Rev. A 45, 1793 (1992)] for a two-level atom in a lossless cavity.

Physical Review A•May 16, 2001•5 citations

Phase operators of the harmonic oscillator and suppression of a number state

C V Sukumar

The phase properties of the quantized electromagnetic field have been studied using operators ${P}^{\ifmmode\pm\else\textpm\fi{}}$ of the harmonic oscillator whose classical analogs are exp(\ensuremath{\mp}i\ensuremath{\theta}), \ensuremath{\theta} being the classical phase. ${P}^{+}$ and ${P}^{\mathrm{\ensuremath{-}}}$ are used to construct a unitary operator ${U}_{p}$(\ensuremath{\alpha})=exp(\ensuremath{\alpha}${P}^{+}$-${\ensuremath{\alpha}}^{\mathrm{*}}$${P}^{\mathrm{\ensuremath{-}}}$) and the properties of the state generated by ${U}_{p}$ from a number state are studied. It is shown that by tuning \ensuremath{\alpha} it is possible to produce a pure state ${\ensuremath{\psi}}_{0}$=${U}_{p}$(\ensuremath{\alpha})\ensuremath{\Vert}0〉 in which a specific number-state component is suppressed.

Physical Review A•Nov 1, 1989•1 citation

Modelling of q-deformed harmonic oscillator on quantum computer

M. I. Samar, V. M. Tkachuk

Physics Letters A•Dec 5, 2024•2 citations
We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the Rabi frequency ${\ensuremath{\Omega}}_{c}$ of the cavity field to that of the Rabi frequency $\ensuremath{\Omega}$ of the driving field. For ${\ensuremath{\Omega}}_{c}<\ensuremath{\Omega}$ and moderate coupling of the transition to the cavity mode the spectral peaks are composed of multiplets. A quantized dressed-atom approach provides a simple explanation of the spectral features and shows that the oscillations in the spectral components arise from the oscillations of the population distribution in the dressed states. The observation of these features would provide evidence for the quantum nature of the cavity field. The distribution is an analog of the harmonic-oscillator probability distribution function, and should be experimentally observable. For ${\ensuremath{\Omega}}_{c}>~\ensuremath{\Omega}$ there is no Autler-Townes splitting and the spectrum is composed of a single peak located at the frequency of the probe transition. We show that this effect results from the collapse of the atom to the ground state, which has been predicted by Alsing, Cardimona, and Carmichael [Phys. Rev. A 45, 1793 (1992)] for a two-level atom in a lossless cavity.
The phase properties of the quantized electromagnetic field have been studied using operators ${P}^{\ifmmode\pm\else\textpm\fi{}}$ of the harmonic oscillator whose classical analogs are exp(\ensuremath{\mp}i\ensuremath{\theta}), \ensuremath{\theta} being the classical phase. P+{P}^{+}P+ and ${P}^{\mathrm{\ensuremath{-}}}$ are used to construct a unitary operator Up{U}_{p}Up​(\ensuremath{\alpha})=exp(\ensuremath{\alpha}P+{P}^{+}P+-${\ensuremath{\alpha}}^{\mathrm{*}}$${P}^{\mathrm{\ensuremath{-}}}$) and the properties of the state generated by Up{U}_{p}Up​ from a number state are studied. It is shown that by tuning \ensuremath{\alpha} it is possible to produce a pure state ${\ensuremath{\psi}}_{0}$=Up{U}_{p}Up​(\ensuremath{\alpha})\ensuremath{\Vert}0〉 in which a specific number-state component is suppressed.