Experimental observation of carrier-envelope-phase effects by multicycle pulses

We present an experimental and theoretical study of carrier-envelope-phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigate the influence of the CEP on the control of phase-dependent multiphoton transitions between the Zeeman sublevels of the ground state of ${}^{87}\mathrm{Rb}$. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities to generate pulses with accuracy that is better than the period of optical oscillations.

Figure 1

Experimental setup. ECDL, external cavity diode laser; AOM, acousto-optic modulator; P, polarizer, PD, photodiode; L, lens. The oven is assembled with the following: 1, copper tube; 2, non-magnetic heater on a magnetic shield; 3, solenoid; 4, pair of Helmholtz coils; and 5, Rb cell.

Figure 2

(a) Time sequence of the laser and the rf pulses to determine the population transfer due to rf excitation. (b) Configuration of the laser and rf pulses along with the longitudinal magnetic field with respect to the Rb cell.

Figure 3

CEP-shaped bichromatic pulses with spectral components of 60 and 100 kHz. The FWHM for both the pulses is 130 $\mu$s with a Gaussian envelope. The unit of the magnetic field is gauss.

Figure 4

(a) Optical probe transmission profile for the one-photon [peaks 1 and 2] and three-photon [peak 3] transitions under the bichromatic rf field excitation. (b) Upper panel: Energy level scheme of ${}^{87}\mathrm{Rb}$. Lower panel: Resonant and non-resonant pathways contributing to a three-photon peak.

Figure 5

Nonlinear dependence of multiphoton excitation on the traverse magnetic field. The unit of the magnetic field is gauss.

Figure 6

Oscillatory nature of the population transfer by changing the phase of one carrier frequency while keeping the other at zero for the bichromatic rf Pulse. (a) (I) Changing the phase ${\varphi }_{100\hspace{0.5em}\text{kHz}}$ and ${\varphi }_{60\hspace{0.5em}\text{kHz}}$$=$ 0 (II) Changing the phase ${\varphi }_{60\hspace{0.5em}\text{kHz}}$ and ${\varphi }_{100\hspace{0.5em}\text{kHz}}$$=$ 0. (b) Effect of the pulse duration T (FWHM) on the population transfer. (I) $T=130\hspace{0.5em}\mu$s, (II) $T=100\hspace{0.5em}\mu$s. Here we changed the phase ${\varphi }_{100\hspace{0.5em}\text{kHz}}$ while keeping ${\varphi }_{60\hspace{0.5em}\text{kHz}}=0$.