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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.


Related in: MedlinePlus

Experimental apparatus for single-photon QW experiments.Frequency-doubled laser pulses at 400 nm and with 140-mW average power, obtained from the fundamental pulses (100 fs) generated by a titanium:sapphire source (Ti:Sa) at a repetition rate of 82 MHz, pump a 3-mm-thick nonlinear β-barium borate crystal (BBO1) cut for type II SPDC (see main text for a definition of all acronyms). Photon pairs at 800 nm generated through this process, cleaned from residual radiation at 400 nm using a long pass filter, pass through an HWP and the BBO2 crystal (cut as BBO1, but 1.5 mm thick) to compensate both spatial and temporal walk-off introduced by BBO1. Next, the two photons are split by a PBS; one is sent directly to the avalanche single-photon detector (APD) D1, whereas the other is coupled into an SMF. At the exit of the fiber, the photon goes through N identical subsequent QW steps (N = 5 in the figure), is then analyzed in both polarization and OAM, and is finally detected with APD D2, in coincidence with D1. Before entering the first QW step, an SLM 1 and an HWP-QWP set are used to prepare the photon initial state in the OAM and SAM spaces, respectively. At the exit of the last step, the polarization projection on the state /φf〉c is performed with a second HWP-QWP set followed by a linear polarizer (LP). The OAM state is then analyzed by diffraction on SLM 2, followed by coupling into a SMF. The projection state /ψf〉w corresponding to each OAM eigenvalue m was thus fixed by the hologram pattern displayed on SLM 2. Before detection, interferential filters (IF) centered at 800 nm and with a bandwidth of 3.6 nm were used for spectral cleaning. As shown in the legend, a single QW step consists of a QWP (optical axis at 45° from the horizontal), a QP with q = 1/2 (axis at 0°), and an HWP (axis at 0°); the HWP was not included in the wavepacket and two-photon experiments.
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Figure 2: Experimental apparatus for single-photon QW experiments.Frequency-doubled laser pulses at 400 nm and with 140-mW average power, obtained from the fundamental pulses (100 fs) generated by a titanium:sapphire source (Ti:Sa) at a repetition rate of 82 MHz, pump a 3-mm-thick nonlinear β-barium borate crystal (BBO1) cut for type II SPDC (see main text for a definition of all acronyms). Photon pairs at 800 nm generated through this process, cleaned from residual radiation at 400 nm using a long pass filter, pass through an HWP and the BBO2 crystal (cut as BBO1, but 1.5 mm thick) to compensate both spatial and temporal walk-off introduced by BBO1. Next, the two photons are split by a PBS; one is sent directly to the avalanche single-photon detector (APD) D1, whereas the other is coupled into an SMF. At the exit of the fiber, the photon goes through N identical subsequent QW steps (N = 5 in the figure), is then analyzed in both polarization and OAM, and is finally detected with APD D2, in coincidence with D1. Before entering the first QW step, an SLM 1 and an HWP-QWP set are used to prepare the photon initial state in the OAM and SAM spaces, respectively. At the exit of the last step, the polarization projection on the state /φf〉c is performed with a second HWP-QWP set followed by a linear polarizer (LP). The OAM state is then analyzed by diffraction on SLM 2, followed by coupling into a SMF. The projection state /ψf〉w corresponding to each OAM eigenvalue m was thus fixed by the hologram pattern displayed on SLM 2. Before detection, interferential filters (IF) centered at 800 nm and with a bandwidth of 3.6 nm were used for spectral cleaning. As shown in the legend, a single QW step consists of a QWP (optical axis at 45° from the horizontal), a QP with q = 1/2 (axis at 0°), and an HWP (axis at 0°); the HWP was not included in the wavepacket and two-photon experiments.

Mentions: In our first experiment, the step operator Û is implemented by a sequence of a QWP, a QP, and a HWP. The QPs have q = 1/2, so as to induce OAM shifts of ±1. Because of reflection losses (mainly at the QP, which is not antireflection-coated), each step has a transmission efficiency of 86% (but adding an antireflection coating could easily improve this value to >95%). The n-step walk is then implemented by simply cascading a sequence of QWP-QP-HWP on the single optical axis of the system. 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. The layout of the apparatus is shown in Fig. 2. A photon pair is generated by spontaneous parametric down-conversion (SPDC) in the product state /H〉/V〉, where H and V stand for horizontal and vertical linear polarization (see the caption of Fig. 2 for details). To carry out a single-particle QW simulation, we split the two input photons with a polarizing beam splitter (PBS); the H-polarized photon only enters the QW setup after being coupled into a single-mode optical fiber (SMF), which sets m = 0. At the exit of the fiber, the initial polarization of the photon is recovered using a QWP-HWP set (not shown in the figure). 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.


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)

Experimental apparatus for single-photon QW experiments.Frequency-doubled laser pulses at 400 nm and with 140-mW average power, obtained from the fundamental pulses (100 fs) generated by a titanium:sapphire source (Ti:Sa) at a repetition rate of 82 MHz, pump a 3-mm-thick nonlinear β-barium borate crystal (BBO1) cut for type II SPDC (see main text for a definition of all acronyms). Photon pairs at 800 nm generated through this process, cleaned from residual radiation at 400 nm using a long pass filter, pass through an HWP and the BBO2 crystal (cut as BBO1, but 1.5 mm thick) to compensate both spatial and temporal walk-off introduced by BBO1. Next, the two photons are split by a PBS; one is sent directly to the avalanche single-photon detector (APD) D1, whereas the other is coupled into an SMF. At the exit of the fiber, the photon goes through N identical subsequent QW steps (N = 5 in the figure), is then analyzed in both polarization and OAM, and is finally detected with APD D2, in coincidence with D1. Before entering the first QW step, an SLM 1 and an HWP-QWP set are used to prepare the photon initial state in the OAM and SAM spaces, respectively. At the exit of the last step, the polarization projection on the state /φf〉c is performed with a second HWP-QWP set followed by a linear polarizer (LP). The OAM state is then analyzed by diffraction on SLM 2, followed by coupling into a SMF. The projection state /ψf〉w corresponding to each OAM eigenvalue m was thus fixed by the hologram pattern displayed on SLM 2. Before detection, interferential filters (IF) centered at 800 nm and with a bandwidth of 3.6 nm were used for spectral cleaning. As shown in the legend, a single QW step consists of a QWP (optical axis at 45° from the horizontal), a QP with q = 1/2 (axis at 0°), and an HWP (axis at 0°); the HWP was not included in the wavepacket and two-photon experiments.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Experimental apparatus for single-photon QW experiments.Frequency-doubled laser pulses at 400 nm and with 140-mW average power, obtained from the fundamental pulses (100 fs) generated by a titanium:sapphire source (Ti:Sa) at a repetition rate of 82 MHz, pump a 3-mm-thick nonlinear β-barium borate crystal (BBO1) cut for type II SPDC (see main text for a definition of all acronyms). Photon pairs at 800 nm generated through this process, cleaned from residual radiation at 400 nm using a long pass filter, pass through an HWP and the BBO2 crystal (cut as BBO1, but 1.5 mm thick) to compensate both spatial and temporal walk-off introduced by BBO1. Next, the two photons are split by a PBS; one is sent directly to the avalanche single-photon detector (APD) D1, whereas the other is coupled into an SMF. At the exit of the fiber, the photon goes through N identical subsequent QW steps (N = 5 in the figure), is then analyzed in both polarization and OAM, and is finally detected with APD D2, in coincidence with D1. Before entering the first QW step, an SLM 1 and an HWP-QWP set are used to prepare the photon initial state in the OAM and SAM spaces, respectively. At the exit of the last step, the polarization projection on the state /φf〉c is performed with a second HWP-QWP set followed by a linear polarizer (LP). The OAM state is then analyzed by diffraction on SLM 2, followed by coupling into a SMF. The projection state /ψf〉w corresponding to each OAM eigenvalue m was thus fixed by the hologram pattern displayed on SLM 2. Before detection, interferential filters (IF) centered at 800 nm and with a bandwidth of 3.6 nm were used for spectral cleaning. As shown in the legend, a single QW step consists of a QWP (optical axis at 45° from the horizontal), a QP with q = 1/2 (axis at 0°), and an HWP (axis at 0°); the HWP was not included in the wavepacket and two-photon experiments.
Mentions: In our first experiment, the step operator Û is implemented by a sequence of a QWP, a QP, and a HWP. The QPs have q = 1/2, so as to induce OAM shifts of ±1. Because of reflection losses (mainly at the QP, which is not antireflection-coated), each step has a transmission efficiency of 86% (but adding an antireflection coating could easily improve this value to >95%). The n-step walk is then implemented by simply cascading a sequence of QWP-QP-HWP on the single optical axis of the system. 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. The layout of the apparatus is shown in Fig. 2. A photon pair is generated by spontaneous parametric down-conversion (SPDC) in the product state /H〉/V〉, where H and V stand for horizontal and vertical linear polarization (see the caption of Fig. 2 for details). To carry out a single-particle QW simulation, we split the two input photons with a polarizing beam splitter (PBS); the H-polarized photon only enters the QW setup after being coupled into a single-mode optical fiber (SMF), which sets m = 0. At the exit of the fiber, the initial polarization of the photon is recovered using a QWP-HWP set (not shown in the figure). 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.

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.


Related in: MedlinePlus