Quantum walks and wavepacket dynamics on a lattice with twisted photons

In the paper

“As a specific demonstration of this feature, we experimentally verified the band structure characterizing a QW; we prepared Gaussian wavepackets of a photon in OAM space, for different values of the average linear quasi-momentum, and observed their free quantum dynamics, governed by the underlying band dispersion relations and the associated topological spin-orbit features (11, 27, 28).”

What the sources say

• Partly supported

  Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [11] Rudner Kitagawa T. M. S., Berg E., Demler E., Exploring topological phases with quantum walks. Phys. Rev. A 82, 033429 (2010). sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [27] Abal G., Siri R., Romanelli A., Donangelo R., Quantum walk on the line: Entanglement and nonlocal initial conditions. Phys. Rev. A 73, 042302 (2006). sourceExperimental — accuracy not yet measured
• Partly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  cites [28] Kitagawa T., Topological phenomena in quantum walks: Elementary introduction to the physics of topological phases. Quantum Inf. Process. 11, 1107– 1148 (2012). sourceExperimental — accuracy not yet measured

In the paper

“In particular, the QP raises or lowers the OAM of the incoming photon according to its SAM state, while leaving the photon in the same optical beam, that is, with no deflections or diffractions.”

What the sources say

• Partly supported

  The discussion on p. 3 says the q-plate produces an outgoing helical wave whose orbital angular momentum has a sign controlled by the input circular polarization; the measurements on p. 5 confirm this for the emerging beam. Our copy does not establish the further assertion that the beam undergoes no deflection or diffraction. (LLM, conf=0.84)

  cites [26] Marrucci L., Manzo C., Paparo D., Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006). 16712234 sourceExperimental — accuracy not yet measured
• Partly supported

  Section 5 gives the q-plate’s single-photon rules: left- and right-circular polarization change OAM by +2q and −2q, respectively. The claim’s absolute ‘no diffractions’ qualification is not supported: section 3 says neglecting transverse diffraction is an approximation and describes diffraction within and beyond the plate. The retrieved passages do not explicitly establish the separate ‘no deflections’ qualification. (LLM, conf=0.87)

  cites [30] Marrucci L., Karimi E., Slussarenko S., Piccirillo B., Santamato E., Nagali E., Sciarrino F., Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications. J. Opt. 13, 064001 (2011). sourceExperimental — accuracy not yet measured
• Partly supported

  Section III states that a tuned q-plate gives the optical field a helical wavefront whose handedness depends on the input circular polarization; Section IV describes the resulting transmitted beam. These passages support the SAM-dependent OAM change, but our copy does not establish the additional claim that there are no deflections or diffractions. No page numbers are available in our copy. (LLM, conf=0.84)

  cites [31] Cardano F., Karimi E., Slussarenko S., Marrucci L., de Lisio C., Santamato E., Polarization pattern of vector vortex beams generated by q-plates with different topological charges. Appl. Opt. 51, C1– C6 (2012). 22505084 sourceExperimental — accuracy not yet measured
• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [32] D’Ambrosio V., Nagali E., Walborn S. P., Aolita L., Slussarenko S., Marrucci L., Sciarrino F., Complete experimental toolbox for alignment-free quantum communication. Nat. Commun. 3, 961 (2012). 22805568 source
• Partly supported

  The Methods section (Q-plate fabrication; page not provided) states that a q-plate changes OAM by +2q or −2q depending on the incoming circular polarization, supporting the SAM-dependent OAM change. The cited passages do not establish that the photon remains in the same optical beam with no deflections or diffractions. The Abstract discusses avoiding diffraction losses from angular masks used for OAM readout, which is a narrower point. (LLM, conf=0.84)

  cites [33] D’Ambrosio V., Spagnolo N., Del Re L., Slussarenko S., Li Y., Kwek L. C., Marrucci L., Walborn S. P., Aolita L., Sciarrino F., Photonic polarization gears for ultra-sensitive angular measurements. Nat. Commun. 4, 2432 (2013). 24045270 PMC3791460 sourceExperimental — accuracy not yet measured

In the paper

“The dispersion relation of quasi-energies ws(k) shows two gapped bands associated with the coin eigenstates |ϕs(k)〉, whereas the parametric dependence of the latter states on k defines the QW topological structure (28).”

What the sources say

• Supported

  The effective-Hamiltonian discussion and Fig. 2 caption (p. 3) describe two quasi-energy bands arising from the walk’s two internal states, with a finite gap for general rotation angles. The same section says the momentum-dependent eigenstate direction n(k) winds around the Bloch sphere and identifies that winding as the origin of the walk’s topological nature. The gap closes at exceptional rotation angles, a qualification to the generic gapped-band description. (LLM, conf=0.92)

  cites [28] Kitagawa T., Topological phenomena in quantum walks: Elementary introduction to the physics of topological phases. Quantum Inf. Process. 11, 1107– 1148 (2012). source

In the paper

“We demonstrate both the QW of single photons and that of two indistinguishable photons, thus highlighting the role of multiparticle quantum interferences.”

In the paper

“The two distributions show a good quantitative agreement, as confirmed by their similarities being higher than 95% (see figure captions for details).”

In the paper

“In the hybrid case, the TVD with the IPT is 13.5 ± 0.7%, to be compared with 21.1 ± 0.7% for the DPT.”

In the paper

“We exploited this feature to investigate the effective band structure of QWs, demonstrating the propagation of Gaussian wavepackets for different points in the Brillouin zone and exploring the associated topological structure arising from the spin-orbit coupling.”

In the paper

“The similarities of the data with the DPT distributions are significantly lower.”

In the paper

“In the standard case, the TVD of the experimental distribution with the IPT one is 6.5 ± 0.9%, to be compared with the TVD of 16.5 ± 0.9% for the DPT model.”

In the paper

“A discrete quantum walk occurs in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons.”

In the paper

“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.”

In the paper

“Here, we implement experimentally the proposal by Zhang et al., thus demonstrating the first photonic QW occurring in a single light beam and using the OAM degree of freedom of photons as discrete walker coordinate”

In the paper

“At the fifth step, the similarities between experimental and theoretical OAM distributions are 98.2 ± 0.4% and 99.0 ± 0.2%, respectively.”

In the paper

“The similarities between experimental and predicted quantum distributions (IPT model) are 98.2 ± 0.4% and 95.8 ± 0.3% for the standard and the hybrid walk, respectively.”

In the paper

“It must be noted, however, that this advantage in scaling remains valid only as long as the entire QW takes place in the optical near-field, where the beam cross-section size will remain approximately constant, whereas in the far-field, the transverse size of the optical components will have to increase with the OAM range (see the Supplementary Materials).”

In the paper

“States belonging to different bands, which correspond to orthogonal polarization eigenstates, propagate in opposite directions, that is, V1(k0) = –V2(k0), highlighting the strong spin-orbit coupling of this system (see Supplementary Materials for more details).”

In the paper

“The V-polarized photon, reflected at the PBS, is sent directly to a detector and provides a trigger, so as to operate the QW simulation in a heralded single-photon quantum regime.”

In the paper

“When A(m) is a slowly varying envelope, these wavepackets are expected to propagate on the 1D lattice with only minimal shape variations and with a speed given by the group velocity Vs(k0)=(dωs/dk)k=k0.”

In the paper

“The associated quasi-momentum has a Gaussian distribution centered on k0 (incidentally, the average quasi-momentum k0 corresponds also to the average azimuthal angle in real space for the optical field distribution within the beam).”

In the paper

“However, the OAM QW platform introduced in this work is also immediately suitable for simulating multiparticle quantum processes, for which quantum interferences cannot be reproduced classically.”

In the paper

“Another potential advantage of the present implementation is the possibility to carry out a full quantum tomography of the outgoing state, which is very challenging for standard interferometric implementations.”

In the paper

“However, the similarity is not a very sensitive test, because it tends to remain high even for fairly different distributions.”

In the paper

“In the implemented setup, the linear distance d between adjacent steps is small compared to the Rayleigh range zR of the photons, that is, d/zR ≪ 1 (near-field regime), so as to avoid optical effects that would alter the nature of the simulated process; a detailed discussion is provided in the Supplementary Materials.”

In the paper

“In the limit of paraxial optics, these two quantities are independent and well defined; the first is associated with the polarization of the light, whereas the second is related to the azimuthal structure of the optical wavefront in the transverse plane (30).”

What the sources say

• Not checked yetcites [30] Marrucci L., Karimi E., Slussarenko S., Piccirillo B., Santamato E., Nagali E., Sciarrino F., Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications. J. Opt. 13, 064001 (2011). source

In the paper

“it allows one to dynamically vary the Hamiltonian system and to measure the whole evolution step by step (not only the final output) without changing the experimental setup.”

In the paper

“In the actual device, the radial profile of the photonic wave function undergoes a small alteration, which however can be approximately neglected in our implementation, as discussed in the Supplementary Materials.”

In the paper

“a very important feature of this QW implementation is the possibility of flexibly preparing arbitrary superpositions or “delocalized” initial states of the walker by exploiting standard holographic optical devices (or, conversely, to make a full quantum tomography of the delocalized output quantum state).”

In the paper

“This proves once more that the measured correlations must be quantum and that they include the effect of multiparticle interference.”

In the paper

“Controlling the quasi-momentum of delocalized quantum states is crucial for carrying out quantum simulations of Bloch-particle dynamics, as shown for instance in (39).”

What the sources say

• Not checked yet

  Checked before — its earlier verdict is held back until a new check runs.

  cites [39] Atala M., Aidelsburger M., Barreiro J. T., Abanin D., Kitagawa T., Demler E., Bloch I., Direct measurement of the Zak phase in topological Bloch bands. Nat. Phys. 9, 795– 800 (2013). source

In the paper

“A similar approach was used to simulate the evolution of a multiband Bloch particle in a time-dependent field, by shining an engineered waveguide array with classical coherent light (37) [see also (38) for a review on discrete-waveguide lattice effects].”

What the sources say

• ?Not checked — no full text of the sourcecites [37] Longhi S., Lobino M., Marangoni M., Ramponi R., Laporta P., Cianci E., Foglietti V., Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization. Phys. Rev. B 74, 155116 (2006). source
• ?Not checked — no full text of the sourcecites [38] Christodoulides D. N., Lederer F., Silberberg Y., Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817– 823 (2003). 12917695 source

In the paper

“We ascribe the residual discrepancies between the observed distributions and the IPT quantum predictions to systematic errors arising from imperfect alignment of the setup.”

In the paper

“In particular, we used only wave plate combinations giving rise to unbiased QWs.”