For the time development of a single system in the quantum jump approach or for quantum trajectories one requires the conditional (reduced) Hamiltonian between jumps and the reset operator after a jump. Explicit expressions for them are derived for a general N -level system by employing the same assumptions as in the usual derivation of the Bloch equations. We discuss a possible minor problem with positivity for these expressions as well as for the corresponding Bloch equations.
Short pulses of a probe laser have been used in the past to measure whether a two-level atom is in its ground or excited state. The probe pulse couples the ground state to a third, auxiliary, level of the atom. Occurrence or absence of resonance fluorescence were taken to mean that the atom was found in its ground or excited state, respectively. In this paper we investigate to what extent this procedure results in an effective measurement to which the projection postulate can be applied, at least approximately. We discuss in detail the complications arising from an additional time development of the two-level system proper during a probe pulse. We extend our previous results for weak probe pulses to the general case and show that one can model an ideal (projection-postulate) measurement much better with a strong than a weak probe pulse. In an application to the quantum Zeno effect we calculate the slow-down of the atomic time development under n repeated probe pulse measurements and determine the corrections compared to the case of n ideal measurements.
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect Itano et al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss in how far the experiment of Itano et al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account. 1
We investigate the interaction of an atom with a multi-channel squeezed vacuum. It turns out that the light coming out in a particular channel can have anomalous spectral properties, among them asymmetry of the spectrum, absence of the central peak as well as central hole burning for particular parameters. As an example plane-wave squeezing is considered. In this case the above phenomena can occur for the light spectra in certain directions. In the total spectrum these phenomena are washed out. PACS numbers: 42.50. Dv, An investigation of resonance fluorescence spectra of atoms interacting with a (single-channel) squeezed vacuum plus a laser was initiated by Carmichael, Lane, and Walls [7] (for further references see the review [3] and Refs. [4,5]). Smart and Swain [8,9] have pointed out the existence of interesting structures in these spectra. In Ref. [11,10] multi-channel squeezing and associated correlation functions for three-level atoms were studied.In this paper we consider the spectral effects of a multi-channel squeezed vacuum in the white noise limit on a two-level atom. For the atomic correlation functions and the total spectrum of all outcoming light a multi-channel squeezed vacuum leads to analogous results as a single-channel squeezed vacuum with appropriate parameters. However, in a multi-channel situation one can observe not only the total spectrum but also the light spectrum in individual channels. It turns out that -due to interference of the (quantized) light scattered from the atom with the squeezed vacuum -these spectra can show unexpected features which are not visible in the total spectrum, e.g., a possible asymmetry, absence of the central peak as well as central hole burning for particular parameters. By the same arguments as in Ref.[2] we expect these features to persist also for only approximate white-noise squeezing.In Section 2 below the general case of multi-channel squeezed white noise interacting with a two-level atom is treated. The spectrum is calculated in terms of a background, scattered, and interference part.In Section 3 we treat in detail an example in which the channels consist of plane waves with fixed directions and polarizations. In this case one has a divergence of the background term when calculated in terms of photon numbers, and we therefore use the spectral Poynting vector to calculate the spectrum for given position and direction of observation of the spectral analyzer. In this case the above phenomena like asymmetry, central hole burning etc. can occur for the light spectra in certain directions.In Section 4 we discuss our results in detail, in particular the question of interference, and point out a possible connection, probably more formal than directly physical, with the results of Ref. [9].
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