QUANTUM STATE MEASUREMENT USING ABSORPTION AND EMISSION SPECTROSCOPY

Abstract

We suggest, a number of spectroscopic techniques to measure quantum state of a radiation field present inside the cavity, For all the schemes we use a system of threelevel at.om with upper two levels driven by quantized field whose state is to be measured. In the first scheme, we utilize the effect of electromagnetically induced transparency to measure the quantum state of the field. This effect prevents the probe field to be absorbed by the atom at the resonant frequency. The combined action of splitting of upper levels and quantum interference of the dressed states while driven by the quantized field , provides the basis for the prevention of absorption of probe field. The absorption spectrum of this system contains the information about photon statistics of the driving field, as the splitting of levels depends upon the number of photons. The information of the photon statistics is extracted from the absorption spectrum and is utilized to get the state of t.he field in the forlll of \iVigner function. We present a realistic picture of the spontaneous emission spectrum by using the relevant definition ofthe spectrum. We do not use any approximations in the calculations of this spectrum unlike the st.eady state spectrum which considers the final limit of time as very large. The model is some what simila,r to the earlier case, where the upper two levels of a three-level atom are driven by a quantized field. The spontaneous emission spectrum contains the information about the photon statistics of the driving field which can be extracted from the spectrum. We reconstruct the Wigner function from the knowledge of the displaced photon statistics of the driving field. The simplicity of the calculations is one of the advantages of the above mentioned schemes. Another advantage of these scheme is that they are independent of the detector efficiency, as we take the single atom observation at. a t.ime. A single no phot.on det.ection can easily be ignored which occurs due to inefficiency of the detect.or. . We further suggest a schel1le for t.he l1leasurement of t.he position dist.ribution of an atom by passillg it. t.hrough a cavity field containing position dependent standing wave of a coherent. field. The determinat.ioll of the position distribution localizes the atom within sub-wavelength of the st,anding wave of the quantized field. The degree of resolution is increased t.o a. large extent. as compared to t.he precision available in the already existing schemes.