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Coherent Driving of a Quantum System with Modulated Free-Space Electrons
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The Quantum Harmonic Oscillator
2023AbstractIn this chapter, we enter the quantum regime. Following a succinct introduction to the topic, we present the main properties of the quantum harmonic oscillator, such as the ground state energy caused by quantum fluctuations, the harmonic energy spectrum of Fock states, coherent states, the density matrix of mixed states and its time evolution ...
Alexander Eichler, Oded Zilberberg
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The Quantum Harmonic Oscillator
2018The oscillator Hamiltonian in the coordinate representation is: $$\hat{H} = {p^{2} \over 2m} +\frac{1}{2} m \omega ^{2} x^{2}.$$
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Quantum entanglement of linearly coupled quantum harmonic oscillators
Physical Review EQuantum harmonic oscillators coupled through coordinates and momenta, represented by the Hamiltonian H[over ̂]=∑_{i=1}^{2}(p[over ̂]_{i}^{2}/2m_{i}+m_{i}ω_{i}^{2}/2x_{i}^{2})+H[over ̂]_{int}, where the interaction of two oscillators H[over ̂]_{int}=ik_{1}x_{1}p[over ̂]_{2}+ik_{2}x_{2}p[over ̂]_{1}+k_{3}x_{1}x_{2}-k_{4}p[over ̂]_{1}p[over ̂]_{2}, are ...
D. N. Makarov, K. A. Makarova
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Anomalous Dissipative Quantum Harmonic Oscillator
Communications in Theoretical Physics, 2008We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as τ−4 and τ ...
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Quantum-Mechanical Harmonic Oscillator
2018Quantum-mechanical treatment of a harmonic oscillator has been a well-studied topic from the beginning of the history of quantum mechanics. This topic is a standard subject in classical mechanics as well. In this chapter, first we briefly survey characteristics of a classical harmonic oscillator.
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The Quantum Mechanical Harmonic Oscillator
1988In Chap. 5 we have treated one-dimensional harmonic and anharmonic oscillations. The harmonic oscillation was characterised by the fact that the oscillation frequency did not depend on the amplitude of the displacement. If we had considered three-dimensional motion we should have found that for the harmonic oscillator all circular and elliptical orbits
Erich W. Schmid +2 more
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Measuring the quantum harmonic oscillator
Frontiers in Optics 2010/Laser Science XXVI, 2010By coupling a superconducting quantum bit to microwave electromagnetic and mechanical resonators, we can demonstrably achieve the resonators’ quantum ground states, and create photon and phonon Fock states, and arbitrary superpositions of photon Fock states.
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Quantum guidelines for solid-state spin defects
Nature Reviews Materials, 2021Gary Wolfowicz +2 more
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Weyl, Dirac and high-fold chiral fermions in topological quantum matter
Nature Reviews Materials, 2021M Zahid Hasan +2 more
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