Experimental realization of quantum walks near synthetic horizons on photonic lattices

A distinct quantum interference peak, whose value is nearly twice that of the distinguishable case, indicates that the two photons are highly indistinguishable.

“As shown in Figs.3(b) and 3(e), a distinct quantum interference peak, whose value is nearly twice that of the distinguishable case, indicates that these two photons are highly indistinguishable [19].”

• cites [19]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionRests on an assumption: If photons are indistinguishable, photon bunching occurs and there is a peak value of coincident counts.

Despite not concentrating at site 0, all theoretical and experimental results reveal that two photons have a trend of bunching toward the Rindler horizon.

“Despite not concentrating at site 0, all these theoretical and experimental results clearly reveal that two photons have a trend of bunching toward the Rindler horizon.”

The paper experimentally realizes quantum walks of entangled photons near an emulated Rindler horizon.

“Here, we propose and experimentally realize quantum walks of entangled photons near an emulated Rindler horizon.”

• Also stated in: § I. INTRODUCTION · plain

  “In this work, we present an observation of the QWs of entangled photons near an emulated horizon.”

The experimental results for the θ = 0 NOON state agree with simulation results, with a similarity of 85.38% ± 0.62%.

“And the experimental results agree with simulation results, as shown in Fig. 4(c), having a similarity of 85.38% ± 0.62%.”

Two indistinguishable photons coupled into different waveguide sites have a larger deviation compared with the case of the same waveguide site.

“Notably, two indistinguishable photons coupled into different waveguide sites have a larger deviation compared with the case of the same waveguide site.”

Under the limited propagation length of z = 400 μm, two photons have a high probability of concentrating around site 2.

“Nevertheless, under the case of the limited propagation length (z = 400 µm), we still find the bunching behavior that two photons have a high probability of concentrating around site 2.”

The quantum walks of two indistinguishable photons exhibit optical trapping near the emulated Rindler horizon.

“We find that the QWs of single photons and two indistinguishable photons exhibit optical trapping near the emulated horizons, which is a well-known classical physical process in which light is trapping around the event horizon.”

• Also stated in: § IV. DISCUSSION · boosted

  “The QWs of single photons and two indistinguishable photons exhibit optical trapping, a well-known classical physical recognition of the light trapping around the horizon.”

Quantum interference near the synthetic horizon leads to a counterintuitive phenomenon of optical escape.

“Remarkably, we find that quantum interference near the synthetic horizon leads to a counterintuitive phenomenon of optical escape.”

• Also stated in: § I. INTRODUCTION · plain

  “Intriguingly, for a certain type of path-entangled photon, there is a counterintuitive phenomenon of optical escape arising from quantum interference.”

• Also stated in: § IV. DISCUSSION · boosted

  “Remarkably, due to the antibunching behavior caused by quantum interference, a counterintuitive phenomenon of optical escape is observed for a certain type of path-entangled photon.”

The quantum walks of single photons exhibit optical trapping near the emulated Rindler horizon.

“We find that the QWs of single photons and two indistinguishable photons exhibit optical trapping near the emulated horizons, which is a well-known classical physical process in which light is trapping around the event horizon.”

• Also stated in: § B. The Green's function of light near Rindler horizon · boosted

  “Both the experimental and the theoretical results validate the trapping process of single photons near the emulated Rindler horizon.”

• Also stated in: § IV. DISCUSSION · boosted

  “The QWs of single photons and two indistinguishable photons exhibit optical trapping, a well-known classical physical recognition of the light trapping around the horizon.”

• AssumptionThe authors state this as an assumption: The quantum walks of single photons can be assumed as the superposition of null geodesics of a massless particle with various transverse vectors.

For the two different injecting cases, the experiment results reveal similarities of 93.0% ± 0.22% and 85.15% ± 0.12% relative to the simulations.

“For these two different injecting cases, the experiment results reveal similarities of 93.0% ± 0.22% and 85.15% ± 0.12% relative to the simulations.”

The deterministically separated identical photon pair has a Hong-Ou-Mandel interference visibility of 97.32% ± 0.17%.

“The inset shows the HOM interference fringe with a visibility of 97.32% ± 0.17%.”

• Also stated in: § Additional information · plain

  “we find that the deterministically separated identical photon pair has a very high visibility of the quantum interferences, characterized by a Hong-Ou-Mandel (HOM) dip with 97.32% ± 0.17% visibility.”

The Gaussian wave packet with transverse wave vector βx = ±π/(2d) has the highest value of velocity in the uniform lattice.

“And the Gaussian wave packet with the transverse wave vector β x = ±π/(2d ) has the highest value of velocity.”

In the uniform photonic lattice, the movement of the center of classical Gaussian wave packets n is linearly proportional to the propagation length.

“And the movement of the center of classical Gaussian wave packets n is linearly proportional to the propagation length [see Figs.5(d1) and 5(d2)].”

The coupling coefficient between adjacent identical waveguides depends on distance as κ ≈ c0 e^{-ηd}, with c0 = 0.3495 μm^-1 and η = 8.456 μm^-1.

“The coupling coefficient depending on the distance between the identical waveguides described as κ ∼ = c 0 e -ηd (c 0 = 0.3495 µm -1 , η = 8.456 µm -1 ).”

• Also stated in: § Additional information · plain

  “The coupling coefficient of the fundamental transverse electric mode at the telecom wavelength between two adjacent identical waveguides is dependent on the distance between them, which can be described as κ ∼ = c 0 e -ηd with c 0 = 0.3495 µm -1 and η = 8.456 µm -1 .”

In the emulated Rindler space, the evolution of the center of a wave packet exponentially depends on the propagation length, n ∝ e^{α sin(βx d)z}.

“In Figs.5(h1) and 5(h2), we can see that the evolution of the center of a wave packet exponentially depends on the propagation length (note that the scale of the vertical axis is logarithmic), which can be depicted as n ∝ e α sin(β x d )z .”

The count rate in site 2 is highest among the output ports.

“Because the count rate in site 2 is highest among the output ports, we hence choose site 2 to measure coincident counts for the two injecting photons.”

The paper experimentally realized quantum walks of single photons, two indistinguishable photons, and entangled photons in a synthetic horizon using silicon photonics.

“In conclusion, we have experimentally realized the QWs of single photons, two indistinguishable photons, and entangled photons in a synthetic horizon using silicon photonics.”

The quantum walks of single photons in the emulated noninertial frame exhibit an accelerated behavior.

“The QWs of the single photons in the emulated noninertial frame exhibit an accelerated behavior.”

The quantum walks of two photons with a long enough propagation length in a photonic lattice have not been achieved.

“Additionally, considering the fabrication level of SOI technology and the brightness of the quantum light source at the current, the QWs of two photons with the long enough propagation length in a photonic lattice have not been achieved.”

For ακ0 z/2 >> 1 (photons propagating a large enough distance), the Green's function simplifies to U_nn ≈ δ(n) exp(i n π/2 - i β0 z).

“when ακ 0 z/2 1, which means photons propagating with large enough distance, one can simplify the Green's function as”

• Also stated in: § APPENDIX B: THE GREEN'S FUNCTION OF THE ACCELERATED LATTICE · plain

  “U nn ≈ 1 2π π -π dk exp(ink)exp in π 2 -iβ 0 z = δ(n)exp in π 2 -iβ 0 z .”

• AssumptionThe authors state this as an assumption: The photonic lattice is described by a tight-binding Hamiltonian with nearest-neighbor coupling and linear coupling coefficients.

The n = 0 waveguide acts as the Rindler horizon.

“And the n = 0 waveguide acts as the Rindler horizon, as shown in Fig. 1(a).”

For a lattice of identical waveguides whose coupling coefficient satisfies κ = αnκ0/2, the evolution of a Gaussian wave packet with an arbitrary transverse wave vector can be depicted as n ∝ e^{α sin(βx d)z}, determined by the acceleration α in the Rindler metric.

“According to transformation optics, we find that for a lattice of identical waveguides whose coupling coefficient satisfies as κ = αnκ 0 /2 (κ 0 is the normalized coupling coefficient), the evolution of a Gaussian wave packet with an arbitrary transverse wave vector can be depicted as n ∝ e αsin(β x d )z , also determined by the acceleration α in the Rindler metric (see Appendix A).”

The quantum walks of photons in the emulated noninertial frame with a Rindler metric can be calculated using the Green's function of the waveguide lattice.

“Since any input state can be expressed with the creation operators a † m and the vacuum state |0 , the QWs of the photons in the emulated noninertial frame with a Rindler metric can be calculated using this type of Green's function.”

The evolution trajectory of light in the Rindler metric is x ∝ e^{±αt}.

“When considering the motion of light, it satisfies null geodesic ds = 0. Then we obtain the evolution trajectory as x ∝ e ±αt .”

The authors' previous work theoretically proposed the use of quantum walks of entangled photons to study quantum interference in a noninertial frame with a Rindler metric emulated by a nonuniform photonic lattice with transformation optics.

“our previous work [54] theoretically proposed the use of the QWs of entangled photons to study quantum interference in a noninertial frame with a Rindler metric that is emulated by a nonuniform photonic lattice with the aid of transformation optics.”

• cites [54]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The coupling coefficients are κ/κ0 = αm/2.

“κ/κ 0 = αm/2.”

The tight-binding Hamiltonian for the accelerated lattice is diagonal in the Bloch-wave representation.

“We obtain that the tight-binding Hamiltonian is diagonal: k |H|k = δ(k -k)H (k),”

• AssumptionThe authors state this as an assumption: The photonic lattice is described by a tight-binding Hamiltonian with nearest-neighbor coupling and linear coupling coefficients.

The (1+1)-dimensional Rindler metric is ds2 = -(αx)2 dt2 + dx2.

“we first map the (1+1)-dimensional Rindler metric [55] into one-dimensional waveguide lattices whose metric is ds 2 = -(αx) 2 dt 2 + dx 2 , (1”

• cites [55]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

This photon escape is completely distinct from the Hawking mechanism that is caused by vacuum fluctuation generating particle pairs with positive and negative energy.

“Just as mentioned in Ref. [54], this photon escape is completely distinct from the Hawking mechanism that is caused by vacuum fluctuation generating particle pairs with positive and negative energy.”

• cites [54]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionRests on an assumption: In the Hawking mechanism, particles with negative energy are captured by the horizon, whereas particles with positive energy escape.

The evolution of photons in the Rindler metric is equivalent to propagation in a medium with effective refractive index n_eff = 1/(αx).

“according to transformation optics, the evolution of photons in the Rindler metric as Eq. ( A1) is equivalent to that propagated in such a medium: n eff = -g 11 /g 00 = 1/αx,”

The uniform photonic lattice can well replicate the null geodesic behavior of photons with different velocity in flat space.

“Therefore, the uniform photonic lattice can well replicate the null geodesic behavior of photons with the different velocity in the flat space.”