Quantum interference in the absorption and emission of single photons by a single ion

We investigate quantum beats in the arrival-time distribution of single photons from a single trapped ${{}^{40}\mathrm{Ca}}^{+}$ ion, revealing their fundamentally different physical origins in two distinct experimental situations: In a $\Lambda$-type level scheme the interference of two 854-nm absorption amplitudes suppresses and enhances the emission process of Raman-scattered 393-nm photons; in a $\mathsf{V}$-type level scheme the interference of two 393-nm emission amplitudes causes a rotation of their dipole emission pattern, resulting in a temporal modulation of the detected photons. For both cases we demonstrate coherent control over the quantum-beat phase through the phases of the atomic and photonic input states, which also allows controlled adjustment of the total photon detection efficiency.

Figure 1

(a) Schematic of the experimental setup: excitation of a single trapped ion with an 854-nm laser beam parallel to the magnetic field axis and polarization-selective detection of 393-nm photons perpendicular to it. HALO stands for high-numerical-aperture laser objective [21], PBS for polarizing beam splitter, and PMT for photomultiplier tube. (b) Level scheme and relevant transitions of the ${{}^{40}\mathrm{Ca}}^{+}$ ion.

Figure 2

(a) The $\Lambda$-shaped three-level system consisting of $|D_{5/2},-\frac{3}{2}\rangle$, $|D_{5/2},+\frac{1}{2}\rangle$, and $|P_{3/2},-\frac{1}{2}\rangle$ including the relevant transitions with their squared Clebsch-Gordan coefficients. (b) The $\mathsf{V}$-shaped three-level system consisting of $|P_{3/2},-\frac{3}{2}\rangle$, $|P_{3/2},+\frac{1}{2}\rangle$, and $|S_{1/2},-\frac{1}{2}\rangle$ including the relevant transitions with their squared Clebsch-Gordan coefficients. Red arrows, absorption of 854-nm photons (${\sigma }^{+}$ and ${\sigma }^{-}$); blue wavy arrows, emission of 393-nm photons; gray arrows, parasitic absorption (854 nm) and emission channels (393 nm).

Figure 3

Arrival-time distribution of single 393-nm photons from an initial coherent superposition (blue circles) and statistical mixture (black dots) in $D_{5/2}$. Red solid line, fit to the data by numerically solving the 18-level optical Bloch equations; green dash-dotted line, exponential fit to the data for the mixture; gray dotted line, exponential fit to the envelope of the oscillation, from which the visibility is determined.

Figure 4

$\Lambda$ scheme. (a) Arrival-time distributions of the 393-nm photons showing quantum beats for two different 854-nm input polarization states, $\left|D\right.〉$ and $\left|A\right.〉$. (b) Arrival-time distributions showing quantum beats for two values, 0 and $\pi$, of the phase ${\Phi }_{\mathrm{D}}\left(0\right)$ of the initial atomic superposition. In (a) and (b), the bin size is 2 ns for 6 min measurement time.

Figure 5

$\mathsf{V}$ scheme. (a) Quantum beats for two different 854-nm input polarization states, $\left|D\right.〉$ and $\left|A\right.〉$. (b) Quantum beats for two values, 0 and $\pi$, of the phase ${\Phi }_{\mathrm{D}}\left(0\right)$ of the initial atomic superposition. The bin size is 2 ns for 10 min measurement time [6 min in (b)].

Figure 6

Quantum-beat visibility in the $\mathsf{V}$ scheme as a function of the initial population in $|D_{5/2},+\frac{3}{2}\rangle$. The data points are calculated from exponential fits to the envelopes of the observed quantum beats.

Figure 7

Suppression and enhancement of the generation efficiency of 393-nm photons controlled via the atomic phase ${\Phi }_{\mathrm{D}}\left(0\right)$. The dots and solid curves (sinusoidal fits) are for short 854-nm excitation pulses (duration $<$ quantum-beat period), while the crosses and dashed curves are for long pulses (duration $\gg$ quantum-beat period). (a) $\Lambda$ scheme: The short photon has about 70 ns duration and 553 ns quantum-beat period, the long photon about 850 ns duration and 106.5 ns quantum-beat period. (b) $\mathsf{V}$ scheme: The short photon extends over $\sim 120$ ns at 277.4 ns beat period; for the long photon the values are 750 and 53.2 ns.

Figure 8

Change of the $D_{5/2}$ population for different 854-nm pulse lengths in the $\Lambda$ scheme. The stairslike behavior results from interference of two excitation amplitudes to $|P_{3/2},-\frac{1}{2}\rangle$. The pulse length is varied in steps of 12.5 ns. The solid line is calculated with the 18-level Bloch equations including experimental parameters. (Inset) Time derivative of the calculated solid line showing the oscillation of the population in $P_{3/2}$, which leads to suppression and enhancement of the photon emission at 393 nm.

Figure 9

Depopulation of $D_{5/2}$ for different 854-nm pulse lengths in the $\mathsf{V}$ scheme, showing simple exponential decay without modulation. The points are measured data; the line is a fit by Bloch equation dynamics. (Inset) Time derivative of the calculated curve [24].

Figure 10

Depopulation of $D_{5/2}$ for different initial phases ${\Phi }_{\mathrm{D}}\left(0\right)$ of the initial superposition, after an excitation pulse of 12.5 ns. The blue dots (solid curve) are measured (calculated) for the $\Lambda$ scheme, the red crosses (dashed curve) for the $\mathsf{V}$ scheme. The Larmor period was 300 ns ($\Lambda$) and 150 ns ($\mathsf{V}$).