Looking into a quantum entanglement

photonic chip By: Keshav Agarwal

To achieve fail-proof secure communication is something various organizations have been trying to

achieve. Industry standard encryption uses 256 bit end-to-end encryption which is virtually impossible

to break using brute-force method. How encrypted communication works between two parties is,

before communication is initiated, the two parties share a key. Then encrypted messages are sent by the

sender and decrypted by the receiver and vice-versa. The security of this key distribution is determined

by the security of key exchanges. The Diffie-Hellman key exchange is one such key exchange which is

used to secure various services over the internet. A research conducted in October 2015 has however

revealed that the Diffie-Hellman key exchange is prone to attack by certain algorithms.

To guarantee that the key is distributed securely between the two parties and to make it impossible for

an eavesdropper to intercept the key without either party knowing is a challenge in cryptography.

This is what Quantum Key Distribution tries to achieve. Quantum key distribution relies on a very

fundamental quantum mechanical principle: Measuring a system, changes the system. And this change

can be detected.

How Quantum Key distribution works in theory is, the sender generates a pair of quantum entangled

photons. The photons can be entangled in either spin or in their phase. These entangled photons are

distributed such that the sender ends up with one photon and the receiver ends up with photon. If an

eavesdropper tries to measures the state of the photon, it will disturb the system and the state

measured by the sender and the receiver will be different. Each photon pair corresponds to one bit. This

is done as many times as deemed necessary (more the number of bits, more the system is secure). Once

the quantum key distribution is completed, the sender and receiver compare their results over a public

communication medium. The number of bits they measured differently is the number of bits stolen by

the eavesdropper. If this number is below a certain limit, information is encrypted using this quantum

key and transmitted to the receiver. If not, the same process is repeated again.

Therefore, Quantum key distributions ensures that the encryption key is distributed safely between the

two parties before communication is initiated.

The Research:

This research tries to achieve Quantum key Distribution using photons which are entangled in phase. As

this phase difference between entangled photon is generated using a time-delay, this kind of

entanglement is called time-bin entanglement.

Time-bin entangled photons are generated and analyzed using the following circuit.

This circuit is basically fifteen tunable Mach-Zehndar interferometers arranged in a particular fashion.

Briefly, the time-bin photons are generated by the Unbalanced MZI labelled as 𝜑𝑝 and analyzed by the

Unbalanced Mach-Zehndar interferometers labelled as 𝜑𝑖 and 𝜑𝑠.

In this paper, it is discussed why and how the interferometers were characterized. Before that, the

working of the Mach-Zehndar interferometer is discussed.

Mach Zehndar Interferometer:

The Mach-Zehndar interferometer is the most important part of the photonic chip. Infact, the chip is

nothing but 15 Mach-Zehndar interferometers configured in a particular fashion. It is what generates

the time-bin entangled photons, demultiplexes the wavelength to separate photon pairs and also

analyses the entangled photons. Without understanding Mach-Zehndar interferometry, it is impossible

to understand the experiment and appreciate its scope.

An ideal Mach-Zehndar interferometer is one in which there is no loss as light propagates. So how one

works is, a beam of light enters at the input and reaches the beam splitter. At the beam splitter, in an

ideal MZI, the beam of light splits into two beams, each having half the power. However, one the beams

has a phase difference of pi imparted to it due to reflection. The two split beams travel through two

separate channels. One of the channels, however has a phase shifter. This phase-shifter is usually a

material of a different refractive index with respect to the propagating medium. So when light travels

through this medium, a phase shift is imparted to it with respect to the other channel. So when the

beams of light interfere at the output, the beams of light from the two channels undergo interference

and the resulting power is a function of the phase shift produced in one of the channels. In an

unbalanced MZI, the length of the two channels are different. Therefore, a phase shift is added not only

in the shorter path due to the phase shifter, but a relative phase shift is also added in the channel with a

longer length as the beam of light travels a longer path. This phase shift is related to the optical path

difference between the two channels. When the two beams interfere at the output, the resulting beam

is again split into 50:50 ratio and passed through two channels. Analysis of power of the beam in of the

channels can be used to calculate the phase shift and thus it can be used to characterize the phase

shifter.

If the phase shifter is tunable, recording the variation of power with the tuned parameter (in this case

voltage of the heater on the idler phase shifter) can be used to find a relation between the tuned

parameter and the phase shift.

Type equation here.

But power is directly proportional to Intensity. Therefore, we expect

power to be periodic with 𝜑

The above description is for when a MZI is used classically, that is, the input is a classical beam of light.

However, in the experiment, the Mach Zehndar Interferometer is used non-classically. That is a beam of

light is not the input but a stream of photons is. However, single photon interference is analogous to

θ

50:50 50:50

𝑦2

𝑦1

(𝑦1 + 𝑦2)′

√2

(𝑦1 + 𝑦2)

√2

Schematic of a Mach Zehnder interferometer

𝑦 →

𝑦1 = 𝐴 sin 𝜔𝑡

𝑦2 = 𝐴 sin(𝜔𝑡 + 𝛼)

𝑦1 + 𝑦2 = 2𝐴 cos𝜑

2sin(𝜔𝑡 +

𝜑

2)

→ 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒(𝑦1 + 𝑦2) = 2𝐴 cos𝜑

2 → 𝐼 = 4𝐴2cos2 𝜑

2 → I=2𝐴2(1 + cos 𝜑)

𝑦 = √2𝐴 sin 𝜔𝑡

classical wave interference where power is analogous to number pf photons. The explanation of the

above phenomena relies on quantum mechanical principles and is beyond the scope of this paper.

Therefore, an interferometer that is to be used non-classically can be characterized classically without

any scope of error.

The Experiment:

The aim of the experiment was to characterize the Mach-Zehnder Interferometer for the idler phase shifter by determining the relationship between the phase shift produced by the waveguide and the Voltage applied. The characterization of the interferometers on chip was essential to make sure that the couplers and the demultiplexers on-chip work correctly and also to characterize the generated pump time-bin photons. Before characterizing the interferometers, it is essential to verify that the input and output couplers

have an effective splitting ratio of 50:50 after considering losses. For doing this, a pulsed laser with a

wavelength of 1557.nm and width of 10ps is input to the input coupler and the two outputs from the

output coupler are fed into a fast oscilloscope. Due to delay in the longer arm, each output contained

double pulses separated at 795ps. The early pulses were from the shorter arm and the late pulses were

from the longer arm. To tune the output coupler to 50:50 splitting, voltage was applied to the heater of

this coupler till the early pulses from both the outputs and the late pulses from both the outputs

became equal. The late pulses and the early pulse of each output were still not equal to each other

because the splitting ratio of the input coupler was still not effectively 50:50. Voltage was applied to the

heater of this coupler until both the pulses became equal in amplitude. It was interesting to note that

splitting ratio of the input coupler was still not 50:50 despite both pulses in both outputs being equal.

This is because, the losses in the longer arm are greater than that in the shorter arm and therefore a

greater power needs to pass through the longer channel to offset this loss. This entire procedure was

done while applying zero volts to the heater of the idler phase shift(𝜑𝑖).

Once this was done, the characterization of the interferometer could be started. For doing this, the

pulsed laser was replaced with a continuous wave laser and one of the outputs of the output coupler

𝜑𝑖

The experimental setup

was fed into a power meter and power readings were taken for different idler phase shift heater

voltages.

Theory:

The heat dissipated in the idler phase shifter per unit time is equal to 𝑉2

𝑅 where V is the voltage applied

to the waveguide and R is its resistance. As it is ensured the max temperature difference between the

chip and the atmosphere is less than 30 degrees, the waveguide loses heat according to Newton’s law of

cooling according to which loss of heat from the waveguide per unit time equals 𝑘𝑇 where k is a

constant and T is the temperature of the waveguide. Therefore, the temperature of the waveguide

varies linearly with 𝑉2. For𝑆𝑖3𝑁4, the refractive index varies directly with temperature, and therefore,

the phase shift imparted to a beam passing through the beam of light varies directly with temperature.

But as temperature varies directly with𝑉2, the phase shift imparted varies directly with 𝑉2. but power

varies periodically with phase shift (eqn 1). Since phase shift varies directly with𝑉2, it implies that power

varies periodically with 𝑉2. Therefore, we expect a periodically relationship between Power and 𝑉2.

Observations:

It was observed that as voltage was increased, power increased, reached a maximum then decreased

and increased again. This power being measured, is the power of the beam resulting from the

interference of light from the shorter and longer arm of the interferometer. This was observed as long

as the voltage was increased. Some periodicity was seen but the Power Vs Voltage graph did not show a

high quality fit with periodic functions like sin and cos.

However, when Power was plotted against 𝑉2, a very high quality fit with cosine was seen.

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10

Po

wer

(uW

)

Voltage

Power Vs Volt1554.96nm

However, when power was plotted against voltage squared for 1559.6nm, a far from perfect periodic fit

was observed.

This was observed because the waveguides on the chip were optimized for 1555nm.

From the Power vs 𝑉2plot for the optimum wavelength (1555nm), it was concluded that power of the

interference beam varies periodically with 𝑉2 and therefore the phase shift produced by the idler phase

shifter varies directly with 𝑉2. This is exactly what was predicted in theory.

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30 40 50 60 70 80 90 100

Po

wer

(uW

)

V^2

Power Vs Voltage Squared1554.96nm

-20

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140 160 180

Po

wer

(uW

)

V^2

Power Vs Voltage Squared1559.64nm

Anomalies:

As Power was plotted against time, a periodic relationship was seen. This could have two implications.

One, the chip had been damaged and the phase shift produced by the waveguide was varying

continuously with time. This would have drastic consequences on the progress of the research. Two, the

laser was hopping between modes. This is due to the rise in temperature of the laser diode during

operation. Due to this rise in temperature, the resonance frequency of the semi-conductor changes

minutely thus changing the wavelength of the laser. This implication would have no effect on the

experiment. When the experiment was done, it was observed that the anomaly was due to laser mode

hopping and not due to damaged chip. One could have arrived at this conclusion by means of a simple

though experiment. If the chip had been damaged, that is, there was a phase variation independent of

voltage in the idler phase shifter, it would have been impossible to tune the input and output couplers

to a perfect 50:50 ratio. As this was not observed, it implied that variation of power with time was

indeed due to laser mode hopping.

0.00E+00

2.00E-05

4.00E-05

6.00E-05

8.00E-05

1.00E-04

0.00E+002.00E+024.00E+026.00E+028.00E+021.00E+031.20E+03

Po

wer

(uW

)

Seconds

Output Power Vs Time

References:

1. Xiong, C., Zhang, X., Mahendra, A., He, J., Choi, D., Chae, C., Marpaung, D., Leinse, A., Heideman,

R., Hoekman, M., Roeloffzen, C., Oldenbeuving, R., van Dijk, P., Taddei, C., Leong, P. and

Eggleton, B. (2015). Compact and reconfigurable silicon nitride time-bin entanglement circuit.

Optica, 2(8), p.724.

2. Adrian, D., Bhargavan, K., Durumeric, Z., Gaudry, P., Green, M., Halderman, J., Heninge, N.,

Springal, D., Thomé, E. and Valenta, L. (2015). Imperfect Forward Secrecy: How Diffie-Hellman

Fails in Practice.

3. Zetie, K., Adams, S. and Tocknell, R. (2000). How does a Mach-Zehnder interferometer work?.

Physics Education, 35(1), pp.46-48.