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Register a new userAn alternate model for protective measurements of two-level systems
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In this article we propose an alternate model for the so called {it protective measurements}, more appropriately {it adiabatic measurements} of a spin 1/2 system where the {it apparatus} is also a quantum system with a {em finite dimensional Hilbert space}. This circumvents several technical as well as conceptual issues that arise when dealing with an infinite dimensional Hilbert space as in the analysis of conventional Stern-Gerlach experiment. Here also it is demonstrated that the response of the detector is continuous and it {it directly} measures {em expectation values without altering the state of the system}(when the unknown original state is a {it nondegenerate eigenstate of the system Hamiltonian}, in the limit of {em ideal} adiabatic conditions. We have also computed the corrections arising out of the inevitable departures from ideal adiabaticity i.e the time of measurement being large but finite. To overcome the {em conceptual} difficulties with a {it quantum apparatus}, we have simulated a {it classical apparatus} as a {em large} assembly of spin-1/2 systems. We end this article with a conclusion and a discussion of some future issues.
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Making measurements on single quantum systems is considered difficult, almost impossible if the state is a-priori unknown. Protective measurements suggest a possibility to measure single quantum systems and gain some new information in the process. Protective measurement is described, both in the original and generalized form. The degree to which the system and the apparatus remain entangled in a protective measurement, is assessed. A possible experimental test of protective measurements is discussed.
We study protective quantum measurements in the presence of an environment and decoherence. We consider the model of a protectively measured qubit that also interacts with a spin environment during the measurement. We investigate how the coupling to the environment affects the two characteristic properties of a protective measurement, namely, (i) the ability to leave the state of the system approximately unchanged and (ii) the transfer of information about expectation values to the apparatus pointer. We find that even when the interaction with the environment is weak enough not to lead to appreciable decoherence of the initial qubit state, it causes a significant broadening of the probability distribution for the position of the apparatus pointer at the conclusion of the measurement. This washing out of the pointer position crucially diminishes the accuracy with which the desired expectation values can be measured from a readout of the pointer. We additionally show that even when the coupling to the environment is chosen such that the state of the system is immune to decoherence, the environment may still detrimentally affect the pointer readout.
We prove a necessary and sufficient condition for the occurrence of entanglement in two two-level systems, simple enough to be of experimental interest. Our results are illustrated in the context of a spin star system analyzing the exact entanglement evolution of the central couple of spins.
Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations
Providing the microscopic behavior of a thermalization process has always been an intriguing issue. There are several models of thermalization, which often requires interaction of the system under consideration with the microscopic constituents of the macroscopic heat bath. With an aim to simulate such a thermalization process, here we look at the thermalization of a two-level quantum system under the action of a Markovian master equation corresponding to memory-less action of a heat bath, kept at a certain temperature, using a single-qubit ancilla. A two-qubit interaction Hamiltonian ($H_{th}$, say) is then designed -- with a single-qubit thermal state as the initial state of the ancilla -- which gives rise to thermalization of the system qubit in the infinite time limit. Further, we study the general form of Hamiltonian, of which ours is a special case, and look for the conditions for thermalization to occur. We also derive a Lindblad-like non-Markovian master equation for the system dynamics under the general form of system-ancilla Hamiltonian.
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