1. Frequency Bin Quantum Photonics
Andrew M. Weiner
Purdue University
with thanks to
P. Imany, J. Jaramillo, O. Odele, M. Alshaykh, H.H. Lu,, N. Lingaraju, A.J. Moore, D.E. Leaird, Minghao Qi [Purdue]
J.M. Lukens and P. Lougovski [ORNL]
Photonics for Quantum Workshop, Rochester Institute of Technology, Jan. 25, 2019

2. Time-Frequency Entangled Photons (Biphotons)
Spontaneous parametric down-conversion (SPDC)
Broadband, continuous spectrum (>5 THz) – but can be filtered to form a discrete spectrum
Frequency correlations
Time correlations
Spontaneous four-wave mixing (SFWM), in a microresonator
Biphoton frequency comb
May be broadband, but made of narrow (discrete) frequency modes
Frequency bin entanglement: analogies to classical WDM?

3. Entanglement in the Optical Frequency Domain
Motivation
Frequencies are robust and compatible with transmission over fibers
Potential for high dimensionality – processing with qudits – more information per photon
Ability to perform routing based on optical frequency
Manipulation in parallel in frequency domain
Chip-scale microresonator sources and potential for further integration
Can be combined with other photon degrees of freedom
Outline
Introduction to frequency-bin entangled photons (biphoton frequency combs)
How to test frequency bin entanglement?
- Some simple applications
Time-frequency hyperentanglement
- Deterministic two-qudit gates in a single photon
Integration potential and conclusion

4. Biphoton comb carved from a continuous spectrum generated via SPDC
Biphoton Frequency Combs
Biphoton comb carved from a continuous spectrum generated via SPDC
Based on chip-scale microresonators, but emphasis on one line pair at a time
Z. Xie, et al.
Nature Photonics 9, 536 (2015)
C. Reimer, et al.
Science 351 ,1176 (2016)

5. Biphoton Frequency Combs (via microring resonators)
Potential for very high dimensional entanglement
Small microring (~380 GHZ FSR)
Larger microring (~50 GHZ FSR)
Strong correlations out to 40th line pair!
Imany, et al, Opt. Exp. 26, 1825 (2018)
Jaramillo, et al, Optica 4, 655 (2017)

6. Nonlocal Dispersion Compensation
Demonstrates frequency-to-time mapping of biphoton combs
~380 GHz Biphoton Frequency Comb – 4 line pairs
Both dispersed: compensation
Undispersed
Signal dispersed
Idler dispersed
Jaramillo, et al, Optica 4, 655 (2017)

7. Biphoton Frequency Comb Entangled State
(frequency basis)
Biphoton wavepacket (delay basis)
Phase coherence across frequency modes?
Structure too fast for single photon detectors
Complex amplitude
(both magnitude and phase)
How to prove the phase coherence for frequency- bin entangled photons?
Sum over frequency bins
Lineshape function

8. Tools for Measuring Frequency Bin Entanglement
Pulse shapers (select frequencies, manipulate spectral phase)
Application to quantum optics
Commercial implementation
Pe’er, Dayan, Friesem, and Silberberg, Phys. Rev. Lett. 94, (2005)
A.M. Weiner, Rev. Sci. Instr. 71, 1929 (2000)
Phase modulators (mix frequencies)
No modulation
Modulate one photon
Modulate both, in phase
Modulate both, out of phase
Manipulating frequency correlations
Weiner is recognized as the pioneer of this field and has been numerous external prizes for this work.
Sensarn, Yin, and Harris, PRL 103, (2009) 8

9. How to Prove Frequency Bin Entanglement?
Use a phase modulator to project a single frequency into multiple sidebands
A phase modulator acts as a frequency mixer, bringing about coherent superpositions of frequency bins for two photon interference
Analogous to wave plates and polarizers used to mix polarization states for studies of polarization entangled photons
Analogous to delay-imbalanced interferometers used to mix time bins for studies of time-bin entangled photons

10. An Interesting Duality
Same components, different order
for characterization of entanglement and for state manipulation
THIS TALK
Imany, et al, Opt. Exp. 26, 1825 (2018);
ibid, Phys. Rev. A 97, (2018)
[Purdue]
Kues et al, Nature 546 (2017) [INRS]
Lukens and Lougovski, Optica 4, 8 (2017) [ORNL]
UPCOMING TALK
(Joe Lukens)
H.-H. Lu, J.M. Lukens, et al., Phys. Rev. Lett. 120, (2018); ibid, Optica 5, 1455 (2018) [Purdue and ORNL]

11. How to Prove Frequency Bin Entanglement?
Use a phase modulator to project a single frequency into multiple sidebands
Creates sidebands (mixes frequencies)
Selects desired signal and idlers, manipulates phases
Selects sidebands, routes to detectors
How to prove stable (coherent) phase?
Biphoton frequency comb
& sweep spectral phase φ1 φ2 φ3
Complex amplitude
(both magnitude
and phase)
Imany, et al, Opt. Exp. 26, 1825 (2018), Phys. Rev. A 97, (2018)

12. We use two different sources of biphoton frequency combs

13. Testing Frequency Bin Entanglement
Adjusting the RF frequency to achieve sideband overlap
(50 GHz microring data)
S6I6 S7I7
Indistinguishability here!
(projection onto a superposition state)
Output of Pulse Shaper 1 S6 S7 I6 I7 ω
π/2
π/2
Coincidences
Phase ω
Output of Pulse Shaper 2
SPD1
SPD2 ω
Imany, et al, “Demonstration of Frequency-Bin Entanglement in an Integrated Optical Microresonator,” CLEO (2017) [postdeadline]
Imany, et al, Opt. Exp. 26, 1825 (2018)

14. Confirming Frequency Bin Entanglement
Phase-dependent two photon interference
Spontaneous parametric down-conversion
𝜓 = 𝑆𝐼 𝑒 𝑖𝜙 𝑆𝐼 𝑒 𝑖2𝜙 𝑆𝐼 3
𝜓 = 𝑆𝐼 𝑒 𝑖 𝜙 𝑆𝐼 2
3 dimensional
2 dimensional
Imany, Odele, et al,
Phys. Rev. A 97, (2018)
Spontaneous four-wave mixing
Quantum state tomography: estimating the density matrix
S6I6 S7I7
𝑉= 93%±13%
2 dimensional
Re (𝜌)
Im (𝜌)
Imany, et al, Opt. Exp. 26, 1825 (2018)
Fidelity: 0.83

15. Extending to Three Frequency Pairs
Imany, et al, Opt. Exp. 26, 1825 (2018)
Biphoton comb from microring
CGLMP inequality (3D Bell inequality)
𝐼 3 =3 𝑃 11 0,0 + 𝑃 21 0,1 + 𝑃 22 0,0 + 𝑃 12 0,0 −
3 𝑃 11 0,1 + 𝑃 21 0,0 + 𝑃 22 0,1 + 𝑃 12 1,0 ≤2
𝑃 𝑎,𝑏 𝑥,𝑦
= 𝐶𝑜𝑖𝑛𝑐. 𝑀𝑎𝑥 𝑐𝑜𝑖𝑛𝑐.
Term
Coincidences
𝑃 11 (0,0)
150±10
𝑃 21 (0,1)
141±23
𝑃 22 (0,0)
152±21
𝑃 12 (0,0)
146±16
Term
Coincidences
𝑃 11 (0,1)
54±4
𝑃 21 (0,0)
33±6
𝑃 22 (0,1)
49±12
𝑃 12 (1,0)
32±10
𝑀𝑎𝑥 𝑐𝑜𝑖𝑛𝑐. =160±18
I3 = 2.63±0.2 (sufficient to establish entanglement for our entangled qutrits)
R. Thew, et al, Phys. Rev. Lett. 93, (2004);
C. Bernhard, et al, J. Phys. A. Math. Theor. 47, (2014).

16. Dispersion Measurement with Biphoton Frequency Comb
Comb sliced from broadband SPDC spectrum
Imany, Odele, et al,
Phys. Rev. A 97, (2018)
Spectral Intensity … …
Phase shift due to fiber dispersion
𝜙 𝑠ℎ𝑖𝑓𝑡 =− 2𝜋 2 𝛽 2 𝐿Δ𝑓 2 𝑓 𝑜𝑠 +Δ𝑓
fos
fos
fos Δf
Freq.
Coincidences vs. frequency for fixed phase
Coincidences vs. phase for fixed frequency bin pair
Slope gives 𝛽 2 =−2.03× 10 −2 p s 2 /m
Expected value of 𝛽 2 =−2.06× 10 −2 p s 2 /m

17. Time Resolution Beyond That From Single-Photon Detectors
Previous work using electro-optic intensity modulators
Lukens, et al, Opt. Lett. 40, 5331 (2015)
Measuring the coincidence rate vs. intensity modulator relative delay
PPLN
Pump
Filters
SMF
1x2
Coupler M1 M2 τ
Coincidence counter
AWG
Coincidences
Improved resolution from ~350 ps to ~70 ps, but lossy
Resolution down to ~1 ps should be possible using phase modulators and frequency bin entanglement
Potential applications
Range-resolved imaging
Stand-off vibrometry
Precision timing acquisition
Large alphabet QKD

18. Time-Frequency Hyper-entanglement
Deterministic optical quantum logic
with multiple high-dimensional degrees of freedom in a single photon
Two-qudit
Single-photon
Deterministic quantum gates
High-dimensional optical quantum logic in large operational spaces
[PURDUE]
Enables construction of deterministic photonic gates, scalable in dimension
Experiments in 3×3 and 16×16 dimensions with a single photon
Readily extended to two photons
Imany, Jaramillo-Villegas , Lukens, Odele, Leaird, Qi, and Weiner, arXiv:
High-dimensional one-way quantum processing implemented on d-level cluster states
[INRS]
Realization and characterization of four-partite, 3 dimensional cluster states via time-frequency encoding of signal-idler pair
Reimer, et al, Nature Physics (2018),

19. Deterministic 2-Qudit Time-Frequency Gates: Experiments
Currently d=3; should scale to higher dimensions
X-gate for 3 time bins
(operation of which conditioned on frequency)
Results in biphoton freq. comb × 3 time bins
Carves d=3 time bins from pump
CINC
SUM
Frequency as control, time as target
Control + target, modulo d
Controlled X-gate
Imany, Jaramillo-Villegas , Lukens, Alshaykh, Odele, Leaird, Qi, and Weiner, arXiv:

20. New: Scaling the Sum Gate to 16 × 16
16 frequency bins, 16 time bins
Equivalent to 8 qubits in a single photon
Frequency as control, time as target
16 ×16 diagonal blocks corresponding to individual frequencies
Control + target, modulo d
Imany, Jaramillo-Villegas , Lukens, Alshaykh, Odele, Leaird, Qi, and Weiner, arXiv:

21. Testing the Coherence of the 2-Qudit SUM Gate
3 frequency bins, 3 time bins
Start with
Frequency bin phase control
Mix frequency bins
Joint spectral intensity after SUM gate
Idler
Time bin phase control
Signal
Sum gate
Mix time bins
State projection
0-1 Interference
1-2 Interference
0-2 Interference
Imany, Jaramillo, Lukens, Alshaykh, Odele, Moore, Leaird, Qi and Weiner, unpublished

22. Potential Application: Qudit Teleportation
Early (1998) qubit teleportation using two degrees of freedom in each photon (polarization and momentum)
Qudit teleportation using time and frequency DoFs of a photon
Only two photons (not three) required!
Poolad Imany (unpublished)
Qudit DFT
Preparer
2-qudit gate
(XOR or SUM)
Proposed experimental realization of the theory from Roa et al, Phys. Rev. A 68, (2003)
Boschi, De Martini, Hardy, and S. Popescu, Phys. Rev. Lett. 80, 1121 (1998)

23. Integrated Frequency Bin Quantum Processor Concept
Beginning to explore thin film LN with SiN (with Prof. Minghao Qi, NSF Quantum RAISE program)
Also exploring Si photonics solutions via AIM Photonics (collaboration with AFRL, RIT, ORNL)
Potential to reduce the loss of bulk optics implementations (~15 dB) to the few dB level
Applicable to both entanglement characterization and quantum frequency processing

24. Programmable Multi-channel Ring Resonator Filters
Simple integrated pulse shapers for photonic RF arbitrary waveform generation
Khan, Shen, Xuan, Zhao, Xiao, Leaird, Weiner, and Qi, Nature Photonics 4, 117 (2010)
Femtosecond pulse
J. Wang, H. Shen, … Weiner, and Qi, Nat. Comm. 6, 5957 (2015)

25. Thanks to many students, collaborators, & sponsors!
Navin Lingaraju
Poolad Imany
Peach Lu
Ogaga Odele
Jose Jaramillo
Minghao Qi