We show that the phase of a field can be determined by incoherent detection of the population of one state of a two-level system if the Rabi frequency is comparable to the Bohr frequency so that the rotating wave approximation is inappropriate. This implies that a process employing the measurement of population is not a square-law detector in this limit. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-frequency transitions. We present a scheme for observing this effect in an atomic beam, despite the spread in the interaction time. 03.67.Hk, 03.67.Lx, 32.80.Qk It is well known that the amplitude of an atomic state is necessarily complex. Whenever a measurement is made, the square of the absolute value of the amplitude is the quantity we generally measure. The electric or magnetic field generated by an oscillator, on the other hand, is real, composed of the sum of two complex components. In describing semiclassically the atom-field interaction involving such a field, one often side-steps this difference by making the so-called the rotating wave approximation (RWA), under which only one of the two complex components is kept, and the counter-rotating part is ignored. Under this approximation, an atom interacting with a field enables one to measure only the intensity, and not the phase of the driving field. This is the reason why most detectors are so-called square-law detectors.In this article, we show how a single atom by itself can detect the absolute phase of a driving field, by making use of the interference between the co-and counter-rotating parts of the excitation, while the Rabi frequency is not negligible compared to the transition frequency. This detection is performed by measuring incoherently the population of either of the two states of a two level atom. This implies that a process employing the measurement of population is not a square-law detector in this limit. We discuss how the sensitivity of the degree of excitation to the phase of the field may enable phase teleportation using a pair of entangled atoms, but poses severe constraints on precise rotations of quantum bits involving low-frequency transitions. We also present a scheme for observing this effect in an atomic beam, despite the spread in the interaction time.We consider an ideal two-level system where a ground state |0 is coupled to a higher energy state |1 . We also assume that the 0 ↔ 1 transitions are magnetic dipolar, with a transition frequency ω, and the magnetic field is of the form B = B 0 cos(ωt + φ). We now summarize briefly two-level dynamics without the RWA. In the dipole approximation, the Hamiltonian can be written as:where g(t) = −g 0 [exp(iωt + iφ) + c.c.] /2, σ i are Pauli matrices, and ǫ = ω corresponds to resonant excitation. The state vector is written as:We perform a rotating wave transformation by operating on |ξ(t) with the unitary operatorQ, where:The Schrödinger equation then takes the form (setti...

Measuring the amplitude and absolute ͑i.e., temporal and initial͒ phase of a monochromatic microwave field at a specific point of space and time has many potential applications, including precise qubit rotations and wavelength quantum teleportation. Here we show how such a measurement can indeed be made using resonant atomic probes via detection of incoherent fluorescence induced by a laser beam. This measurement is possible due to self-interference effects between the positive-and negative-frequency components of the field. In effect, the small cluster of atoms here act as a highly localized pickup coil, and the fluorescence channel acts as a transmission line.

We demonstrate an atomic interferometer in which the atom passes through a single-zone optical beam, consisting of a pair of bichromatic counter-propagating fields. During the passage, the atomic wave packets in two distinct internal states trace out split trajectories, guided by the optical beams, with the amplitude and spread of each wave-packet varying continuously, producing fringes that can reach a visibility close to unity. We show that the rotation sensitivity of this continuous interferometer (CI) can be comparable to that of the Borde-Chu Interferometer (BCI). The relative simplicity of the CI makes it a potentially better candidate for practical applications. 39.20.+q, 03.75.Dg, 32.80.Pj

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Abstract:We present a technique to stabilize to an atomic transition the chirping frequency of a narrow-band semiconductor diode laser. The technique is demonstrated to chirp-cool the 85 Rb atoms used for loading a magneto-optical trap. The stabilization process eliminates long term fluctuations and drifts in the number of atoms caught in the trap. This is an extremely simple, easy-to-implement, and robust method for wide range of laser cooling experiments employing frequency chirping. 2Cooling and trapping of atoms [1] is of considerable current interest. In laser cooling experiments atoms scatter resonant photons from a laser beam directed against the velocity of the atomic beam. The transfer of photon momentum to the atom eventually brings the atom to rest. The primary experimental difficulty in such atom-slowing techniques is the varying Doppler shift experienced by the atom as it slows down. The change in the Doppler shift takes the atom out of resonance with the laser field. Therefore, to keep the atom in resonance with the applied field as it slows down, either the atomic or the laser frequency needs to be smoothly and accurately varied. The technique based on varying the atomic frequency is called Zeeman cooling [2], while the corresponding technique based on varying the laser frequency is called chirp cooling [3][4][5][6]. In the latter technique the laser is tuned below the zero-velocity resonance frequency of the moving atom. As the atom slows, the Doppler shifts decrease, and therefore, to keep the atom in resonance, the laser frequency must increase. This is achieved by sweeping (or chirping) the laser frequency as a function of time at a rate equal to the ratio of the Doppler shift at the most probable velocity of the incoming atom to the total stopping time for the atom.To chirp cool the atoms, diode lasers are preferred, not only because of their compactness and low cost [7][8][9], but also because chirp is easier to achieve with diode lasers. Diode lasers, however, suffer from the frequency drift caused by changes in the junction temperature, by current noise and by the perturbation of the external cavity length. This drift will cause drifting of the chirp, which results in inefficient cooling. Furthermore, it will cause drifting of the end points of the chirp, leading to fluctuations in the final velocity profile of the atomic beam.This problem can be overcome by using, for example, an acousto-optic modulator (AOM). Briefly, the diode laser frequency is shifted by the AOM, and then locked to an atomic transition using standard methods [10][11][12][13]. The AOM driving frequency is then scanned in order to produce the required chirping. One drawback of this approach is that the direction of the output of an AOM is correlated with the driving frequency, so that the 3 scan is accompanied by undesired angular variations. One can overcome this problem by using a compensating, scanning mirror. However, in order for this process to work well, the scan range should be a small fraction of the base freq...