Figure 1

The intensity (left panel of each pair) and phase (right panel) distribution of several LG modes and their superpositions.Reuse & Permissions

Figure 2

(a) Energy levels of ${}^{87}\mathrm{Rb}$, and the associated laser frequencies. (b) Schematic of experimental setup: SLM, spatial light modulator; SMF, single-mode fiber; SPCM, single-photon-counting module. Circularly polarized write and read pulses illuminate the ${}^{87}\mathrm{Rb}$ MOT (Magnet-Optical Trap), and circularly polarized Stokes and anti-Stokes photons are selectively directed onto the SPCMs passing through quarter-wave plates and polarizers. The pair of SLM and SMF serves as a spatial mode filter. (c) Coincidence rate and time-resolved coincidence (inset) between the Stokes and anti-Stokes photons of the ${\mathrm{LG}}_{0,0}$ mode as a function of the time delay.Reuse & Permissions

Figure 3

Gaussian components of applied phase modulations $T(x,y)$ to an incoming Gaussian beam of waist $w_0=2.2\mathrm{mm}$. (a) $T(x,y)=e^{i\arg [x-x_0+i(y-y_0)]}$. The left panel plots the simulation while the right panel shows the experimental result. (b) $T(x,y)=e^{i\arg (x-x_0+iy)}$. (c) $T(x,y)=e^{i(\pi /2)\mathrm{sgn}(x-x_0)}$. In panels (b) and (c), the dots are experimental results, and the solid curves are obtained from the numerical simulation.Reuse & Permissions

Figure 4

Graphical representation of the density matrix ${\rho }_{\exp }$ of a state as estimated by quantum state tomography from the experimentally obtained coincidences. The upper plot is the real part, and the lower plot is the imaginary part.Reuse & Permissions