The planar gradiometer consists of a directly coupled magnetometer inductively coupled to the smaller loop of an asymmetric, two-loop flux transformer patterned in a single film of YBa2Cu3O7−x. The coupling is adjusted mechanically to balance the gradiometer to about 1 part in 3000 with respect to fields perpendicular to its plane. The baseline is 48 mm and the intrinsic balance with respect to in-plane fields about 1 part in 1400. When a magnetic field is applied solely to the magnetometer, its sensitivity is reduced by only 5% by the presence of the flux transformer.
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We measure phase-dependent fluorescence spectra of two-level atoms driven by a monochromatic laser field, for off-resonance excitation. Pairs of spectra with phases of opposite sign are found to display striking differences that arise entirely from time ordering.[S0031-9007 (97)03685-5] PACS numbers: 32.80. -t, 42.50.LcTime ordering arises naturally in quantum mechanics and is explicit in the well known Dyson expansion for the time translation operator [1]. Physically, time ordering enforces causality in the measurement process: a measurement at time t can affect the quantum state and hence the possible outcomes of future measurements at times t 0 . t. In photodetection, this has the consequence that the intensity correlation functions that correctly describe measurements of optical fields at multiple times must be both normal and time ordered [2]. Thus, it is possible to view time ordering in quantum optics as a consequence of the photodetection process. Alternatively, time ordering in photodetection can be viewed as a consequence of fluctuations in the vacuum field [3,4]. In this picture, vacuum fluctuations provide a formal description of photons, leading to shot noise and atom-field interactions that are discrete in time.In this Letter, we show that phase-dependent resonance fluorescence spectra dramatically exhibit the consequences of time ordering in the detection of photons from atomic systems. Phase-dependent resonance fluorescence spectra are obtained by homodyne detection of scattered radiation from free atoms that are irradiated by a quasiresonant field. The radiation field E of the atoms is mixed with a local oscillator (LO) field jE LO je if having a controllable fixed phase f relative to the field that drives the atoms. The interference between the LO and atom radiation fields then leads to fluctuations in the detected power that are determined by the quadrature operatorThe spectrum of the detected power fluctuations is measured with a spectrum analyzer for different LO phases f. We find that quadrature spectra for phases of f 645 ± are strikingly different when the driving field is offresonance, and we show that this difference is entirely due to time ordering. The phase-dependent power spectrum (with the shot noise of the LO removed) is the Fourier transform of the correlation function C f ͑t͒ ͗:x f ͑t 2 ͒x f ͑t 1 ͒:͘, where t 2 t 1 1 t and : : denotes normal ordering. The angled brackets denote a quantum statistical average and a time average over t 1 . Two types of two-time field correlation functions appear in C f ͑t͒. The first are of the form ͗Ê y ͑t 2 ͒Ê ͑t 1 ͒͘ 1 c.c. which are phase independent. Here, the time ordering is determined by the normal ordering. These lead to ordinary resonance fluorescence spectra. Of particular interest are the phase-dependent terms of the form e 22if ͗Ê ͑t 2 ͒Ê ͑t 1 ͒͘ 1 c.c. Here, the time ordering is not determined by normal ordering.The field operatorÊ ͑t͒ can be considered to contain both a source field (atom) contributionÊ S and a free vacuum fieldÊ V . ...
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