Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation

Abstract

Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.

Two-dimensional fluorescence-detected coherent spectroscopy with absolute phasing by confocal imaging of a dynamic grating and 27-step phase-cycling

“…Since the first demonstration of linear FDCS with phaselocked pulses, 33-35 also known as "phase-locked spontaneous light emission" (PLSLE), 36 it has been implemented in numerous applications, e.g., control of photo-ionization 37 and photo-fragmentation, 38 quantum state holography and reconstruction, [39][40][41] interference of vibrational wave-packets in isolated single-molecules, 21 fluorophore discrimination, 42 etc. For a two-level system, a comparison of the double-sided Feynman diagrams for linear absorption with that for linear FDCS is shown in Figure 1.…”

Probing weak dipole-dipole interaction using phase-modulated nonlinear spectroscopy

“…This approach has been demonstrated in 2D electronic spectroscopy [6] but also in electronic wave packet interferometry [7]. In the latter scheme, one records the signal from an observable (such as fluorescence intensity, photocurrent or photoionization [7][8][9]) emitted by the particles subject to two short laser pulses with a specific time-delay and a slowly modulated relative phase. Demodulation with respect to this relative phase and a subsequent Fourier transformation with respect to the time-delay yield a complex-valued spectrum.…”

Multidimensional coherent optical spectroscopy of semiconductor nanostructures: a review

“…Signal isolation can be advantageously performed by lock-in amplification. Interestingly, the lock-in reference can be generated such as to reduce the impact of mechanical fluctuations in the setup, providing enough phase stability for the Fourier transformation, without the need of active stabilisation [75]. In the implementation of Tekavec et al, the lock-in reference is produced by sending the auxiliary outputs of the Mach-Zehnder interferometers through monochromators.…”

“…To achieve undersampling using pulse-shaping methods, the frequency of the rotating frame is set by a proper phasing of the excitation pulses [35] . In experiments where a frequency selection of the signal is achieved using lock-in amplification (Section 3.2.3), a "physical" undersampling is achieved [75]. The signal evolves, as a function of time delays, in a rotating frame centred at the lock-in reference frequency.…”

“…The signal evolves, as a function of time delays, in a rotating frame centred at the lock-in reference frequency. Indeed, in this case the demodulated signal evolves at the difference frequency between the optical frequency of the physical signal and of the reference (given by the monochromator wavelength in Refs [75,74] or by the cw reference laser in Ref [71]). Let us underline, though, that all these undersampling methods do not increase the bandwidth of the experiment: for a given delay step size, the bandwidth is always the same, only the centre of the spectral range is shifted.…”