On Quantum Jump in Quantum Mechanics

Quantum mechanics had been considered as a theory of ensembles for a long time since its foundation.However,quantum jumps demonstrated in atomic system after 1980s leads to new approaches,such as quantum jumps approach,that can be used to describe the trajectory of single quantum system.Here we summarized our recent efforts to develop quantum jump approach to the Josephson-tunnel-junction based superconducting qubits.We experimentally demonstrated quantum jumps in a macroscopic quantum system.In addition,quantum jumps can serve as a useful tool to investigate the properties of the two-level systems that are ubiquitous in solid-state systems.Quantum mechanics had been considered as a theory of ensembles for a long time since its foundation.However,quantum jumps demonstrated in atomic system after 1980s leads to new approaches,such as quantum jumps approach,that can be used to describe the trajectory of single quantum system.Here we summarized our recent efforts to develop quantum jump approach to the Josephson-tunnel-junction based superconducting qubits.We experimentally demonstrated quantum jumps in a macroscopic quantum system.In addition,quantum jumps can serve as a useful tool to investigate the properties of the two-level systems that are ubiquitous in solid-state systems.

Progress in physicsJan 1, 20090 citations

On the Theory of Quantum Jumps

Gerard Nienhuis

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 19870 citations

Tests for nonrandomness in quantum jumps

Dana J. Berkeland, Daisy A. Raymondson, V. M. Tassin

In a fundamental test of quantum mechanics, we have observed $228 000$ quantum jumps of a single trapped and laser cooled $^{88}\mathrm{Sr}^{+}$ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze $238 000$ quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short- or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.In a fundamental test of quantum mechanics, we have observed $228 000$ quantum jumps of a single trapped and laser cooled $^{88}\mathrm{Sr}^{+}$ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze $238 000$ quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short- or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.

arXiv:physics/0304013Physical Review AMay 7, 200423 citations

Are there quantum jumps

David K. Ferry

Generally, one thinks of a “quantum jump” as the process in which an electron “jumps” between a pair of quantum states, even as the process is treated within perturbation theory. This jump of an electron has remained a key point of conservative (i.e., traditional) quantum mechanics. But, the question of the time dependence of such a transition, e.g. the time for an atom to be ionized by radiation, is somewhat different than this view. A detailed approach in which an incoming wave first polarizes the quantum states and then completes the transition has allowed for a detailed discussion of the smooth transition of the electron from one state to the next. Here, we will discuss the history of the process, and illustrate the approach with the question of “how long does it take for an electron to emit a phonon?” The entire process arises from the proper application of wave mechanics and obviates the need to even consider a discussion of quantum jumps.Generally, one thinks of a “quantum jump” as the process in which an electron “jumps” between a pair of quantum states, even as the process is treated within perturbation theory. This jump of an electron has remained a key point of conservative (i.e., traditional) quantum mechanics. But, the question of the time dependence of such a transition, e.g. the time for an atom to be ionized by radiation, is somewhat different than this view. A detailed approach in which an incoming wave first polarizes the quantum states and then completes the transition has allowed for a detailed discussion of the smooth transition of the electron from one state to the next. Here, we will discuss the history of the process, and illustrate the approach with the question of “how long does it take for an electron to emit a phonon?” The entire process arises from the proper application of wave mechanics and obviates the need to even consider a discussion of quantum jumps.

International Journal of Modern Physics Conference SeriesJan 1, 20140 citations

In a fundamental test of quantum mechanics, we have observed

228 000

quantum jumps of a single trapped and laser cooled

^{88}\mathrm{Sr}^{+}

ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze

238 000

quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short- or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.