Ramsey interference in a multilevel quantum system

We report Ramsey interference in the excitonic population of a negatively charged quantum dot measured in resonant fluorescence. Our experiments show that the decay time of the Ramsey interference is limited by the spectral width of the transition. Applying a vertical magnetic field induces Zeeman split transitions that can be addressed by changing the laser detuning to reveal two-, three-, and four-level system behavior. We show that under finite field the phase-sensitive control of two optical pulses from a single laser can be used to prepare both population and spin states simultaneously. We also demonstrate the coherent optical manipulation of a trapped spin in a quantum dot in a Faraday geometry magnetic field.

Figure 1

(a) A $\frac{\pi }{2}$ pulse creates a coherent superposition of the excited and ground states; the Bloch vector is rotated by $\frac{\pi }{2}$ about the $x$ axis. (b) The system undergoes free evolution; the Bloch vector precesses about the $z$ axis. (c) A second $\frac{\pi }{2}$ pulse maps the system into the excited or ground state dependent on the time delay between the pulses; the Bloch vector is rotated by $\frac{\pi }{2}$ about the $x$ axis. (d) An illustration of the energy levels of the negatively charged QD at zero magnetic field. (Bloch spheres were produced with [12].)

Figure 2

(a) A pulsed Hanbury-Brown and Twiss $g^{\left(2\right)}\left(\tau \right)$ measurement. (b) The rotation of the Bloch vector about the $x$ axis. (c) Rabi oscillations. (d) An illustration of our experimental setup for performing RI. (e) (Red) Interference visibility of input laser pulses. (Black) The visibility of the Ramsey fringes as a function of pulse separation. (f) Emission intensity as a function of fine time delay at a short pulse separation (50 ps). (g) Emission intensity as a function of fine time delay at a longer pulse separation (1000 ps).

Figure 3

(a) An illustration of the allowed transitions and energy levels in a Faraday geometry magnetic field. (b) A beating in the Ramsey fringe visibility at 125 mT magnetic field. The gray exponential decay is a fit to the decay envelope of the two-level system as in Fig. 2. (c) Measured intensity and a function of laser detuning.

Figure 4

(a) A sketch of the three-level system considered in the model. (b) The measured emission intensity of the three-level system as a function of pulse separation at 500 mT. (c) The expectation value of the ground state electron spin in the long time limit as a function of pulse separation. (d) A full simulation of the expected emission intensity as a function of pulse separation. (e) The same simulation as (d), but here the effect of the pulse separation-dependent spin preparation is neglected. (f) The same simulation as (d) but here the coherence terms between the two electron ground states are rapidly destroyed.

Figure 5

(a) Experimental measurement of Ramsey fringes at half the laser field amplitude used in Fig. 4. (b) Experimental measurement of Ramsey fringes at twice the laser field amplitude used in Fig. 4. (c) A simulation of (a). (d) A simulation of (b).