Electronically programmable photonic molecule

May combine two claims.

The two optical modes are separated by 2μ = 2π × 7 GHz and have cavity linewidths of γ = 2π × 96 MHz, corresponding to a loaded (intrinsic) quality factor of Q = 1.9×10^6 (Q_i = 2.5×10^6).

“In our case, the two optical modes are separated by 2 µ = 2 π × 7 GHz and have cavity linewidths of γ = 2 π × 96 MHz, corresponding to a loaded (intrinsic) quality factors of Q = 1 . 9 × 10 6 ( Q i = 2 . 5 × 10 6 ), thus forming a wellresolved two-level system (Fig. 1c).”

May combine two claims.

The DC Stark effect can be achieved by applying a DC electric field to the two-level system, blue-shifting one ring and red-shifting the other, resulting in an anti-crossing curve due to optical coupling.

“DC Stark effect can be achieved by applying a DC electric field to the two-level system. The DC field blue-shifts one ring and red-shifts the other one. The resulting transmission spectra show an anti-crossing curve due to the optical coupling between the two rings.”

May combine two claims.

The authors demonstrate a photonic molecule with two distinct energy levels and control it by external microwave excitation.

“In this work, we demonstrate a photonic molecule with two distinct energy-levels and control it by external microwave excitation.”

• Also stated in: § Electronically Programmable Photonic Molecule · p. 1 · plain

  “In this work, we overcome the existing performance trade-off paradigm and realize a programmable photonic two-level system that can be dynamically controlled using gigahertz microwave signals (Fig. 1a).”

May combine two claims. The quote only partly states this claim.

The observed Rabi oscillation and Ramsey interference are in excellent agreement with theoretical predictions.

“The measurements are in excellent agreement with theoretical predictions (see Supplementary).”

May combine two claims.

The paper demonstrated coherent and dynamic control of a two-level photonic molecule with microwave fields and on-demand photon storage and retrieval.

“Our demonstration of the coherent and dynamic control of a two-level photonic molecule with microwave fields and on-demand photon storage and retrieval paves a path to a new paradigm of control over photons.”

May combine two claims.

The S (AS) mode spatially spans both optical cavities, with the light in the two cavities being in- (out-of-) phase.

“The S (AS) mode spatially spans both optical cavities, with the light in the two cavities being in- (out-of-) phase.”

May combine two claims.

In the bright-dark mode limit, one mode is mainly localized in the first ring and is optically bright and accessible to the input optical waveguide, while the other mode is mainly localized in the second ring and is optically dark and decoupled from the input optical waveguide by geometry.

“In this limit, one of the modes is mainly localized in the 1st ring (purple in Fig. 4a), and thus is still accessible to the input optical waveguide and is optically bright, while the other mode is mainly localized in the 2nd ring (black in Fig. 4a) and thus is decoupled from the input optical waveguide by geometry and becomes optically dark (See Supplementary for details).”

• Also stated in: § Electronically Programmable Photonic Molecule · p. 5 · plain

  “As a result, bright mode can be accessed from the optical waveguide, while the dark mode cannot (forbidden by geometry).”

May combine two claims.

A large range of Rabi frequencies is achievable with low applied voltages, in excellent agreement with theoretical predictions.

“We find a large range of Rabi frequencies achievable with low applied voltages (Fig. 3a) to be in excellent agreement with theoretical predictions (Fig. 3b and Supplementary).”

May combine two claims.

The optical coherence time is ∼1.6 ns for both Rabi and Ramsey oscillations, in agreement with the cavity decay time.

“The optical coherence time is ∼ 1 . 6 ns for both Rabi and Ramsey oscillations in agreement with the cavity decay time.”

May combine two claims.

A dark mode lifetime of 2 ns is extracted, which is about two times the lifetime of the critically coupled bright mode.

“Tracking the intensity of the retrieved optical pulses stored in the dark mode, we extract a dark mode lifetime of 2 ns, which is about two times of the lifetime of the critically coupled bright mode as expected (Fig. 4d).”

• Also stated in: § Electronically Programmable Photonic Molecule · p. 5 · plain

  “Inset: the extracted intensity of the retrieved light shows nearly twice the lifetime of the critically coupled bright mode.”

May combine two claims.

The optical lifetime of the two-level system is ∼1.6 ns, much shorter than the coherence time of the laser (∼μs).

“As the optical lifetime of the two-level system ( ∼ 1.6 ns) is much shorter than the coherence time of the laser ( ∼ µ s)”

May combine two claims.

Once the microwave signal is turned off, the photons are trapped in the dark mode and become decoupled from the waveguide, leaving cavity intrinsic dissipation as the only photon loss mechanism.

“Once the microwave signal is turned off, the photons are trapped in the dark mode and become decoupled from the waveguide leaving cavity intrinsic dissipation as the only photon loss mechanism.”

May combine two claims.

The phase coherence time of the two energy levels obtained in the Ramsey measurement is dominated by cavity dissipation, in good agreement with that obtained from the Rabi oscillation.

“As the optical lifetime of the two-level system ( ∼ 1.6 ns) is much shorter than the coherence time of the laser ( ∼ µ s), the phase coherence time of the two energy levels obtained in this measurement is dominated by cavity dissipation in good agreement with that obtained from the Rabi oscillation.”

May combine two claims.

For a lithium niobate ring resonator fabricated close to its material loss limit (Q ~ 10^9), with δω = 20 GHz, μ = 1 GHz, θ = 0.05, and γex1 = 2 GHz, a tunable delay of more than 800 ns with a minimum of 500 ps steps and over 95% efficiency could be achieved.

“As an example, assuming a lithium niboate ring resonator can be fabricated close to its material loss limit ( Q ∼ 10 9 ), set δω = 20 GHz, µ = 1 GHz so θ = 0 . 05, and let γ ex1 = 2 GHz, one could achieve a tunable delay of more than 800 ns with a minimum of 500 ps steps (limited by output coupling bandwidth) and over 95% efficiency.”

• AssumptionThe authors state this as an assumption: A lithium niobate ring resonator can be fabricated close to its material loss limit (Q ~ 10^9).

May combine two claims.

Electro-optic methods are ideally suited for controlling photonic two-level systems since they have fast response, can be programmed and allow for large scale integration.

“Electro-optic methods [15-21] are ideally suited for controlling photonic two-level systems since they have fast response, can be programmed and allow for large scale integration.”

• cites [15] Guo, X., Zou, C.-L., Jung, H. & Tang, H. X. On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes. Phys. Rev. Lett. 117, 123902 (2016). sourceNot checked yet

  Not checked in the free run.

• cites [16] Sato, Y. et al. Strong coupling between distant photonic nanocavities and its dynamic control. Nat. Photon. 6, 56–61 (2012). sourceNot checked yet

  Not checked in the free run.

• cites [17] Clemmen, S., Farsi, A., Ramelow, S. & Gaeta, A. L. Ramsey interference with single photons. Phys. Rev. Lett. 117, 223601 (2016). sourceNot checked yet

  Not checked in the free run.

• cites [18] Xu, Q., Schmidt, B., Pradhan, S. & Lipson, M. Micrometre-scale silicon electro-optic modulator. Nature 435, 325–327 (2005). sourceNot checked yet

  Not checked in the free run.

• cites [19] Ayata, M. et al. High-speed plasmonic modulator in a single metal layer. Science 358, 630–632 (2017). sourceNot checked yet

  Not checked in the free run.

• cites [20] Shambat, G. et al. Ultra-low power fiber-coupled gallium arsenide photonic crystal cavity electro-optic modulator. Opt. Express 19, 7530–7536 (2011). sourceNot checked yet

  Not checked in the free run.

• cites [21] Enami, Y. et al. Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients. Nat. Photon. 1, 180–185 (2007). sourceNot checked yet

  Not checked in the free run.

May combine two claims.

A static resonator can be used to slow down the propagation of a photon, but such slow-down is fundamentally limited by the frequency bandwidth of the resonator (delay-bandwidth product) and cannot be controlled on-demand.

“While a static resonator can be used to slow down the propagation of a photon, such slow-down is fundamentally limited by the frequency bandwidth of the resonator, i.e. the delay-bandwidth product, and cannot be controlled on-demand.”

May combine two claims.

Fast phase modulators can generate new optical frequencies but do not support distinct and long-lived optical modes.

“For example, fast phase modulators [9, 23] can generate new optical frequencies but they do not support distinct and long-lived optical modes.”

• cites [9] Lin, Q., Xiao, M., Yuan, L. & Fan, S. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension. Nat. Commun. 7, 13731 (2016). sourceNot checked yet

  Not checked in the free run.

• cites [23] Wade, M. T., Zeng, X. & Popović, M. A. Wavelength conversion in modulated coupled-resonator systems and their design via an equivalent linear filter representation. Opt. Lett. 40, 107–110 (2015). sourceNot checked yet

  Not checked in the free run.

May combine two claims.

The use of a dynamically-modulated resonator system can overcome the delay-bandwidth product constraint, enabling new functionalities such as optical buffering.

“In contrast, the use of a dynamically-modulated resonator system can overcome the delay-bandwidth product constraint, enabling new functionalities such as optical buffering [36].”

• cites [36] Casanova, J., Romero, G., Lizuain, I., García-Ripoll, J. J. & Solano, E. Deep strong coupling regime of the Jaynes–Cummings model. Phys. Rev. Lett. 105, 263603 (2010). sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Dynamically controlled two- and multi-level photonic systems have the potential to enable novel photonic technologies including topological photonics, advanced photonic computation concepts and on-chip optical quantum systems.

“Considering the high versatility and scalability of dynamically controlled two- and multi-level photonic systems, they have the potential to enable novel photonic technologies including topological photonics [3], advanced photonic computation concepts [21, 37] and on-chip optical quantum systems [9, 10].”

• cites [3] Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014). sourceNot checked yet

  Not checked in the free run.

• cites [21] Enami, Y. et al. Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients. Nat. Photon. 1, 180–185 (2007). sourceNot checked yet

  Not checked in the free run.

• cites [37] Yanik, M. F. & Fan, S. Stopping light all optically. Phys. Rev. Lett. 92, 083901 (2004). sourceNot checked yet

  Not checked in the free run.

• cites [9] Lin, Q., Xiao, M., Yuan, L. & Fan, S. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension. Nat. Commun. 7, 13731 (2016). sourceNot checked yet

  Not checked in the free run.

• cites [10] Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011). sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

With microwave control and possible integration of on-chip photonic components including filters, routers and modulators, a new generation of photonic-electronic systems with advanced functionalities can be put in practice.

“With microwave control and the possible integration of onchip photonic components including filters, routers and modulators, a new generation of photonic-electronic systems with advanced functionalities can be put in practice.”

Probably not a substantial claim: may not pass S2 (checkable).

These results represent the initial step towards integrated electro-optic coherent manipulation of photonic states and energies.

“These results represent the initial step towards integrated electro-optic coherent manipulation of photonic states and energies, and could have immediate applications in signal processing and quantum photonics.”

May combine two claims.

When the microwave frequency detuning to the two-mode resonances is much larger than the driving strength (δ ≫ Ω), the microwave modulation behaves as a weak perturbation and induces a shift of the optical energy levels.

“When the microwave frequency detuning to the two-mode resonances is much larger than the driving strength (i.e. δ ≫ Ω), the microwave modulation behaves as a weak perturbation. This perturbation induces a shift of the optical energy levels.”

• AssumptionThe authors state this as an assumption: The nanophotonic two-level system under a coherent microwave drive can be described by the given Hamiltonian.

May combine two claims.

Electrically active photonic platforms based on silicon, III-V materials, plasmonics, graphene, and polymers allow for fast electro-optic modulation at gigahertz frequencies, but suffer from dramatically reduced photon lifetimes compared to passive platforms.

“Electrically active photonic platforms based on silicon [16], III-V materials [12, 20], plasmonics [17], graphene [19], and polymers [28] allow for fast electro-optic modulation at gigahertz frequencies, but suffer from dramatically reduced photon lifetimes compared to passive platforms.”

• cites [16] Sato, Y. et al. Strong coupling between distant photonic nanocavities and its dynamic control. Nat. Photon. 6, 56–61 (2012). sourceNot checked yet

  Not checked in the free run.

• cites [12] Chen, W., Özdemir, Ş. K., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192–196 (2017). sourceNot checked yet

  Not checked in the free run.

• cites [20] Shambat, G. et al. Ultra-low power fiber-coupled gallium arsenide photonic crystal cavity electro-optic modulator. Opt. Express 19, 7530–7536 (2011). sourceNot checked yet

  Not checked in the free run.

• cites [17] Clemmen, S., Farsi, A., Ramelow, S. & Gaeta, A. L. Ramsey interference with single photons. Phys. Rev. Lett. 117, 223601 (2016). sourceNot checked yet

  Not checked in the free run.

May combine two claims.

The longer dark mode lifetime is expected because the bright mode lifetime is affected by waveguide coupling, while the dark mode lifetime is determined by intrinsic losses only, as it is decoupled from the input waveguide.

“This is expected since the lifetime of the bright mode is affected by the waveguide coupling, while the lifetime of the dark mode is determined by the intrinsic losses of the resonator only, as it is decoupled from the input waveguide.”

May combine two claims.

The observed Rabi oscillation corresponds to a rotation along the real axis of the energy Bloch sphere and indicates that light tunnels back and forth between the two optical modes at two different optical frequencies.

“The observed Rabi oscillation corresponds to a rotation along the real axis of the energy Bloch sphere (Fig. 3c, inset) and indicates that light tunnels back and forth between the two optical modes at two different optical frequencies.”

May combine two claims.

In the case of a bright-dark optical mode pair (high bias voltage, μ ≪ δω), c1 is composed by a large part of a1 with a small part of a2, and c2 has a large part of a2 with only a small part of a1.

“whereas in the case of a birght-dark optical mode pair, i.e. the bias voltage is high µ ≪ δω , a 1 , a 2 have a large frequency difference and in c 1 , c 2 basis, c 1 is composed by a large part of a 1 with small part of a 2 and c 2 has large part of a 2 while has only small part of a 1 .”

• AssumptionThe authors state this as an assumption: The nanophotonic two-level system under a coherent microwave drive can be described by the given Hamiltonian.

May combine two claims.

For c1, c2, the microwave modulation has a component that induces an exchange interaction and a component that induces a frequency modulation.

“This Hamiltonian indicate that for c 1 , c 2 , the microwave modulation has a component that induces an exchange interaction c 1 c † 2 + c † 1 c 2 and a component that induces a frequency modulation c † 2 c 2 -c † 1 c 1 .”

• AssumptionThe authors state this as an assumption: The nanophotonic two-level system under a coherent microwave drive can be described by the given Hamiltonian.

May combine two claims.

At large bias voltages, the access of mode c2 to the external waveguide is effectively controlled by the microwave drive Ω, and the lifetime for mode c2 becomes closer to that of the intrinsic cavity lifetime.

“From these equations of motion, we see that at large bias voltages, γ ex 2 → 0 and the access of mode c 2 to the external waveguide is effectively controlled by the microwave drive Ω. At the same time, the life time for mode c 2 becomes closer to that of the intrinsic cavity life time.”

• AssumptionThe authors state this as an assumption: The nanophotonic two-level system under a coherent microwave drive can be described by the given Hamiltonian.

May combine two claims.

The conversion term is finite and suppressed by a factor sin θ = μ/δω, and the frequency modulation term is large but can be neglected under the high-Q approximation; the resulting Hamiltonian still has a similar form to the bright mode pairs, with a pre-factor sin θ in conversion efficiency.

“Here the conversion term is finite and is suppressed by a factor sin θ = µ δω and the term Ω cos( ω m t ) cos θ ( c † 2 c 2 -c † 1 c 1 ) is large, meaning that c 1 , c 2 are being frequency modulated. However, Since the modulation frequency is orders of magnitudes larger than the bandwidth of the optical modes, we can neglect this term under highQ approximation. The resulting Hamiltonian still has”

• AssumptionThe authors state this as an assumption: The nanophotonic two-level system under a coherent microwave drive can be described by the given Hamiltonian.
• AssumptionThe authors state this as an assumption: The high-Q approximation allows neglecting the frequency modulation term.