Angular momentum transport with twisted exciton wave packets

A chain of cofacial molecules with $C_N$ or $C_{Nh}$ symmetry supports excitonic states with a screwlike structure. These can be quantified with the combination of an axial wave number and an azimuthal winding number. Combinations of these states can be used to construct excitonic wave packets that spiral down the chain with well-determined linear and angular momenta. These twisted exciton wave packets can be created and annihilated using laser pulses, and their angular momentum can be optically modified during transit. This allows for the creation of optoexcitonic circuits in which information, encoded in the angular momentum of light, is converted into excitonic wave packets that can be manipulated, transported, and then reemitted. A tight-binding paradigm is used to demonstrate the key ideas. The approach is then extended to quantify the evolution of twisted exciton wave packets in a many-body, multilevel time-domain density functional theory setting. In both settings, numerical methods are developed that allow the site-to-site transfer of angular momentum to be quantified.

Figure 1

Twisted exciton (TX) wave packets. A TX wave packet travels down a chain of molecules with $C_7$ or $C_{7h}$ symmetry. Colors represent the evolving phase of the quantum amplitudes, here depicted as a continuum, although these are discrete in practice.

Figure 2

Three-arm $H_2$ sites. (a) A single site is composed of a triad of $H_2$ dimers that lie in the plane of a disk of radius $R$. Each $H_2$ has a bond length of 1.40 Bohr. (b) Laser excitation from the left induces a Rabi oscillation in a pair of sites.

Figure 3

Exciton band structure (tight binding). Exciton energies as a function of linear momentum index $k_e$ and angular momentum index $q_e$ EAM for a 51-site chain of seven-arm molecules. Here, ${\tau }_{\mathrm{arm}}=0.75\mathrm{\Delta }$ and ${\tau }_{\mathrm{chain}}=0.1\mathrm{\Delta }$. The solid blue curves are a guide to the eye.

Figure 4

Change of excitonic angular momentum on a chain (TB). Left panels shows the AM transfer reaction $\mathrm{GS}+2_p=2_e$ (top) and final excitonic state (bottom). Right panels show AM addition (top) associated with $2_e+(-1_p)=1_e$ and final excitonic state (bottom). Colors represent the phase of the quantum amplitudes which have been linearly interpolated.

Figure 5

Changing the EAM of a chain. The upper panel shows the initial wave-packet 51-site chain of seven-arm molecules with central wave-number index of $k_e=13$. A cw laser ($-1_p$) is used to change the EAM of the packet as it moves along the ring of molecules. The curves are each associated with a particular longitudinal wave-number index $k_e$ and collectively comprise the components of the packet with EAM $=2$ (red) and those associated with a $\mathrm{EAM}=1$ (blue). Parameters: ${\tau }_{\mathrm{arm}}=0.75\mathrm{\Delta }$ and ${\tau }_{\mathrm{chain}}=0.1\mathrm{\Delta }$. The associated linear momenta are $\hslash 2\pi k_e/\left(La\right)$, where $a$ is the longitudinal spacing between molecules and $L$ is the number of molecules.

Figure 6

Evolution of TX wave packet. Time slices for total exciton population of each molecule on 50-site chain. Blue-filled curve shows original packet on periodic ring of sites, while a red-filled red curve is generated by a twisted laser pulse at the left end of a finite chain. The overlap is essentially perfect, and this is depicted with a red/blue pattern. ${\tau }_{\mathrm{arm}}=0.75\mathrm{\Delta }$.

Figure 7

Phase maps for TX wave packet. Top panel: ${\tau }_{\mathrm{arm}}=0$. Bottom panel: ${\tau }_{\mathrm{arm}}=0.75\mathrm{\Delta }$. The thick black lines are from the theoretical predictions of Eqs. (33) and (34).

Figure 8

Cyclic TX motion in a two-site, three-arm $H_2$ system with $R=3.78$ Bohr. (a) Spin $+1$ laser pulses are applied to the left end of the two-site system of Fig. 2. Twisted excitons with EAM $=1_e$ are generated on the left site (blue dots) and oscillate to the right site (green triangles). Populations of EAM $=-1_e$ on both sites are denoted with purple dots. The points are connected as a guide to the eye. (c) Plot of the corresponding energy manifold and eigenstate populations. Envelope parameters are $\{t_0=408,\tau =81.6,\omega =0.390,E_0=0.002\}$ in a.u. (b),(d) Same analysis but now with laser intensity that is five times greater, $E_0=0.010$ a.u.

Figure 9

TX transfers in a two-site, three-arm $H_2$ system with $R=1.89$ Bohr. (a),(b) A spin-1 laser pulse is applied on one site and a TX with EAM $=1_e$ is generated on that site (blue dots). The population of EAM $=1_e$ on the second site is denoted by green triangles. And the population of EAM $=-1_e$ on both sites is in purple. (c),(d) The corresponding energy manifold and populations of eigenstates of (a) and (b), respectively. Envelope parameters are $\{t_0=408,\tau =54.4,\omega =0.375,E_0=0.005\}$ and $\{t_0=408,\tau =54.4,\omega =0.375,E_0=0.010\}$ in a.u., respectively.

Figure 10

20-site chain of three-arm $H_2$ sites. A chain of 20 cofacial sites, separated by $a=10.2$ Bohr and with arm radius $R=3.78$ Bohr, is excited from the left by an optical vortex pulse. The resulting TX packet is shown in Fig. 11.

Figure 11

TX transport in the 20-site, three-arm $H_2$ system. Isosurface visualization of exciton transport with electron component (green) and hole component (red) densities of $0.005/{\mathrm{Bohr}}^3$. Envelope parameters are $\{t_0=408,\tau =81.6,\omega =0.390,E_0=0.002\}$ in a.u.