Shelved optical electron amplifier: Observation of quantum jumps

Nagourney, Warren; Sandberg, J.; Dehmelt, Hans

doi:10.1103/physrevlett.56.2797

Cited by 904 publications

(525 citation statements)

References 12 publications

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“…The statistical interpretation highlights the fact that quantum mechanics provides us only with probabilities [9,10,11,28,29,31,52,58]. Although a probabilistic theory may produce some predictions with certainty, most quantities that we deal with at the microscopic scale are subject to statistical fluctuations: expectation values, correlations at a given time, or autocorrelations at different times when we observe for instance the successive transitions of a trapped ion [307,308]. Exact properties of individual systems can be found only in special circumstances, such as the ideal measurement of some observable (section 11).…”

Section: Interpretation Of Probabilities and Statistical Ensembles Ofmentioning

confidence: 99%

“…of particle detectors or of avalanche processes, deserve to be studied through models. Measurements of a more elaborate type, in which some quantum property of S is continuously followed in time, are now being performed owing to experimental progress [307,308,361,362,319]. 152 In the Schrödinger picture, the expectation value of any (time-independent) observable for the subensemble E i was found from the stateD i of Eq.…”

Section: Other Types Of Measurementsmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Interpretation Of Probabilities and Statistical Ensembles Ofmentioning

confidence: 99%

Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…The evolution of each trajectory is decomposed into two alternating steps: unitary evolution of the wave function and the reduction of the state (quantum jump) to one of its components due to the interaction with the environment. The quantum jump method has its historical roots in the old hypothesis of Niels Bohr concerning the nature of atomic transitions and to the von Neumann's hypothesis of the (nonlinear) reduction of the state in the measurement process but it is also related to direct observations [29,30] of jumps in dynamics of trapped ions driven by laser beams. The quantum jump method reduces the computational effort because one replaces the evolution of density matrix (linear, but size N 2 problem) by the evolution of the wave function (nonlinear, but only size N problem).…”

Section: Linear Vs Nonlinearmentioning

confidence: 99%

On the linearity of the Schrödinger equation

Bialynicki‐Birula¹

2005

Braz. J. Phys.

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“…This is achieved with low-power photoionization light sources and low-flux atomic beams. Only for trapping of rare isotopes, slightly higher rates may be necessary to beat charge exchange processes with 40 Ca from the atomic beam [4].…”

Section: Introductionmentioning

confidence: 99%

Two-color photoionization of calcium using SHG and LED light

et al. 2010

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We present a photoionization method to load single 40 Ca ions in a linear Paul trap from an atomic beam. Neutral Ca I atoms are resonantly excited from the ground state to the intermediate 4s4p 1 P 1 -level using coherent 423nm radiation produced by single-pass second harmonic generation in a periodically poled KTiOPO 4 crystal pumped with an 120mW extended cavity diode laser. Ionization is then attained with a high-power light emitting diode imaged to the trap center, using an appropriately designed optical system composed of standard achromatic doublet lenses. The setup simplifies previous implementations at similar efficiency, and it hardly requires any maintenance at all.

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Shelved optical electron amplifier: Observation of quantum jumps

Cited by 904 publications

References 12 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

On the linearity of the Schrödinger equation

Two-color photoionization of calcium using SHG and LED light

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