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Quantum walks and wavepacket dynamics on a lattice with twisted photons.

Cardano F, Massa F, Qassim H, Karimi E, Slussarenko S, Paparo D, de Lisio C, Sciarrino F, Santamato E, Boyd RW, Marrucci L - Sci Adv (2015)

Bottom Line: Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space.Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets.Our demonstration introduces a novel versatile photonic platform for quantum simulations.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, Napoli 80126, Italy.

ABSTRACT
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.

No MeSH data available.


Wavepacket propagation in a five-step QW.(A and B) Experimental results, showing the step-by-step evolution of the OAM distribution of a single photon prepared in a Gaussian wavepacket with σ = 2, in the SAM band s = 1 (summed over different polarizations). (A) and (B) correspond to the two cases k0 = π (maximal group velocity) and k0 = π/2 (vanishing group velocity), respectively. The latter configuration shows some spreading of the Gaussian envelope, governed by the group velocity dispersion. Poissonian statistical uncertainties at ±1 SD are shown as transparent volumes. (C and D) Theoretical predictions corresponding to the same cases. At the fifth step, the similarities between experimental and theoretical OAM distributions are 98.2 ± 0.4% and 99.0 ± 0.2%, respectively. The color scale reflects the number of steps.
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Figure 4: Wavepacket propagation in a five-step QW.(A and B) Experimental results, showing the step-by-step evolution of the OAM distribution of a single photon prepared in a Gaussian wavepacket with σ = 2, in the SAM band s = 1 (summed over different polarizations). (A) and (B) correspond to the two cases k0 = π (maximal group velocity) and k0 = π/2 (vanishing group velocity), respectively. The latter configuration shows some spreading of the Gaussian envelope, governed by the group velocity dispersion. Poissonian statistical uncertainties at ±1 SD are shown as transparent volumes. (C and D) Theoretical predictions corresponding to the same cases. At the fifth step, the similarities between experimental and theoretical OAM distributions are 98.2 ± 0.4% and 99.0 ± 0.2%, respectively. The color scale reflects the number of steps.

Mentions: In Fig. 4, we report the experimental “real-time” (that is, step-by-step) observation of these propagating packets for a five-step QW. These data refer in particular to the band s = 1, with k0 = π and k0 = π/2, corresponding to maximum and vanishing group velocities, respectively, with a step operator implemented by a QP plus a QWP. Next, we proceeded to explore the whole irreducible Brillouin zone by varying the average quasi-momentum k0 in steps of π/8 across the (0, π) range. At each value of k0, in order to obtain a single wavepacket propagation, the SAM input state must be prepared in the eigenstate /ϕ1(k0)〉, corresponding to a specific elliptical polarization. As a result of the so-called sublattice or chiral symmetry (11), the corresponding SAM (or coin) eigenstates of these wavepackets describe a maximum circle in the Poincaré polarization sphere, as illustrated in Fig. 5A. The number of full rotations of the vector /ϕ1(k)〉 on the sphere, as k varies from –π to π, is a topological property of the QW system. In our case, we observe a single full rotation (we actually see half a rotation, as we tested only half of the Brillouin zone), thus verifying the topological class of our system. Other topological QW phases could be realized by modifying the QW step operator Û, as discussed in (11). We then determined the group velocity of these wavepackets by measuring the mean OAM exit value after five steps, as shown in Fig. 5B. The whole OAM distribution for some of these points is also shown in Fig. 5 (C to G).


Quantum walks and wavepacket dynamics on a lattice with twisted photons.

Cardano F, Massa F, Qassim H, Karimi E, Slussarenko S, Paparo D, de Lisio C, Sciarrino F, Santamato E, Boyd RW, Marrucci L - Sci Adv (2015)

Wavepacket propagation in a five-step QW.(A and B) Experimental results, showing the step-by-step evolution of the OAM distribution of a single photon prepared in a Gaussian wavepacket with σ = 2, in the SAM band s = 1 (summed over different polarizations). (A) and (B) correspond to the two cases k0 = π (maximal group velocity) and k0 = π/2 (vanishing group velocity), respectively. The latter configuration shows some spreading of the Gaussian envelope, governed by the group velocity dispersion. Poissonian statistical uncertainties at ±1 SD are shown as transparent volumes. (C and D) Theoretical predictions corresponding to the same cases. At the fifth step, the similarities between experimental and theoretical OAM distributions are 98.2 ± 0.4% and 99.0 ± 0.2%, respectively. The color scale reflects the number of steps.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4643825&req=5

Figure 4: Wavepacket propagation in a five-step QW.(A and B) Experimental results, showing the step-by-step evolution of the OAM distribution of a single photon prepared in a Gaussian wavepacket with σ = 2, in the SAM band s = 1 (summed over different polarizations). (A) and (B) correspond to the two cases k0 = π (maximal group velocity) and k0 = π/2 (vanishing group velocity), respectively. The latter configuration shows some spreading of the Gaussian envelope, governed by the group velocity dispersion. Poissonian statistical uncertainties at ±1 SD are shown as transparent volumes. (C and D) Theoretical predictions corresponding to the same cases. At the fifth step, the similarities between experimental and theoretical OAM distributions are 98.2 ± 0.4% and 99.0 ± 0.2%, respectively. The color scale reflects the number of steps.
Mentions: In Fig. 4, we report the experimental “real-time” (that is, step-by-step) observation of these propagating packets for a five-step QW. These data refer in particular to the band s = 1, with k0 = π and k0 = π/2, corresponding to maximum and vanishing group velocities, respectively, with a step operator implemented by a QP plus a QWP. Next, we proceeded to explore the whole irreducible Brillouin zone by varying the average quasi-momentum k0 in steps of π/8 across the (0, π) range. At each value of k0, in order to obtain a single wavepacket propagation, the SAM input state must be prepared in the eigenstate /ϕ1(k0)〉, corresponding to a specific elliptical polarization. As a result of the so-called sublattice or chiral symmetry (11), the corresponding SAM (or coin) eigenstates of these wavepackets describe a maximum circle in the Poincaré polarization sphere, as illustrated in Fig. 5A. The number of full rotations of the vector /ϕ1(k)〉 on the sphere, as k varies from –π to π, is a topological property of the QW system. In our case, we observe a single full rotation (we actually see half a rotation, as we tested only half of the Brillouin zone), thus verifying the topological class of our system. Other topological QW phases could be realized by modifying the QW step operator Û, as discussed in (11). We then determined the group velocity of these wavepackets by measuring the mean OAM exit value after five steps, as shown in Fig. 5B. The whole OAM distribution for some of these points is also shown in Fig. 5 (C to G).

Bottom Line: Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space.Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets.Our demonstration introduces a novel versatile photonic platform for quantum simulations.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, Napoli 80126, Italy.

ABSTRACT
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.

No MeSH data available.