Thrust II: Distribution of entanglement at telecom wavelengths.

Vision: This thrust of the project will be dedicated to engineer new experiments that will allow the expansionof the quantum repeater concepts presented above, towards functionality at telecom wavelengths and longerdistances in fiber links. The BNL team (Figueroa, Katramatos, Nomerotski, and Stankus)will demonstrate a portable high rate entanglement source compatible with quantum memory operation. Additionally, they will also demonstrate experiments in which the same room temperature technology used in the quantum memories can be used to convert the wavelength of the entangled photons from 795nm to the telecom O-band window.

Vision for Thrust II: QLAN2 Telecom Long Distance Operation}: A portable high repetition rate entangled source, compatible with quantum memories will be finalized in BNL. Frequency conversion units based on the room temperature quantum memories will also be developed. The produced telecom wavelength entanglement will be distributed in long fiber links provided by ESNet and Crown Castle. One long distant path will connect SBU and BNL. Other possible path will connect BNL and the colocation facility at 71 Clinton Road in Garden City, NY.

Portable source of entangled photons. A new design for a portable quantum entanglement source in which all the laser sources and parametric down conversion units are rack mounted is currently under development in the QIST laboratory in BNL. In order to produce polarization entanglement, the simultaneous resonant condition for both H and V polarized photons will be satisfied by placing and tuning two PPKTP crystals in an amplification cavity.

We propose to create high repetition polarization entangled states |\Psi\rangle = 1/\sqrt{2}(|HH\rangle + |VV\rangle) by pulsing the pump laser. Improvements to the entanglement generation rate will be achieved by finding the optimal reflectivity of the out-coupling mirror in the OPA cavity to find a compromise between finesse and cavity output. We will efficiently match the production of SPDC photon pairs to the main mode of the cavity in real time, thereby achieving maximum finesse square enhancement setup. A notable advantage of this source is that it can be easily converted from a DV entangled source to a CV quantum source by exchanging the PPKTP non linear crystals. The source can easily generate squeezed light tuned to atomic lines  or Schrödinger kitten states by combination with single photon subtraction.

Development of frequency conversion units. Having low-noise light-matter interfaces in which quantized fields can be manipulated (as demostrated above) is the perfect springboard towards designing the next generation of devices needed for long distance quantum repeater operation. In this part of the project, the BNL team will use the room temperature quantum memory systems developed in SBU (already available in the BNL QIST laboratory) for the distinct purpose of frequency conversion. The SBU team has experience in the frequency manipulation of probe fields under Electromagnetically Induced Transparency (EIT) conditions. They have recently achieved the wavelength conversion between the rubidium D1 and D2 lines through the use of adiabatic transfer using double-lambda schemes with conversion efficiencies \sim10%.

Frequency conversion using Rubidium atoms. (a) Frequency conversion between the Rb D1 and D2 lines after storage and retrieval with different control fields (795nm: solid yellow, 780nm: solid blue in inset) forming a Double-lambda configuration . Input pulse: dashed red, 795nm: solid red, 780nm: solid green. (b) atomic diamond scheme to achieve conversion from 795nm (solid red) to 1324nm or 1367nm (solid blue) using pump I at 780nm and pump II at 1324nm or 1367nm (solid green).

Frequency conversion to telecom wavelengths at the single photon level. In order to create the essential photons at telecommunication wavelengths, we will use nonlinear down conversion in rubidium using a diamond scheme in the room temperature quantum light matter interfaces. This system requires a photon input at 795nm (such as the entanglement produced in the available sources), and two pumps at 780 and 1324nm or 1367nm in order to generate a photon at a telecommunication wavelength of 1324nm or 1367nm. The BNL group will develop and optimize this capability in the room temperature quantum memories at the single-photon-level for reversible inputs at 795 or 1324nm or 1367nm. These experiments will allow to increase the propagation distance of entanglement in the experiments using ESnet long fiber loops in the BNL campus.

Long distance entanglement distribution using ESnet fiber links. Having sources of entanglement that are bridged to operate at telecom wavelengths will open possibilities to explore the distribution of entanglement over long distances. The current fiber infrastructure already available to our collaboration includes fiber loops in the BNL campus provided by ESnet that can connect the SDCC facility to the QIST laboratory using fiber distances of up to 96km. Additionally, we are in a negotiation process with ESnet to establish use of fiber pairs connecting the SDCC to the colocation facility at 71 Clinton Road in Garden City, NY, providing access to an excellent test-bed to analyze the propagation of entanglement over a long distance. Furthermore, the connection to SBU using fiber provided by Crown Castle Fiber can also be tested.

Our procedure to evaluate the quality of entanglement propagation will be as follows: using a density matrix \rho=|{\psi}\rangle \langle {\psi}|, after projection of the two photons by polarizers with angles \alpha and \beta (located in remote locations), we will obtain an expectation value for the measurements of coincidences after long distance propagation: P_{VV}(\alpha,\beta)=\text{Tr}\{\rho\hat{M}_{\alpha\beta}\}=c_0+c_1\cos2\beta+c_2\sin2\beta. Here, the operator \hat{M}_{\alpha\beta}=|{V_\alpha V_\beta}\rangle \langle {V_\alpha V_\beta}| denotes the projection onto a vertical polarization state. In the basis of crystals generating the entanglement, we have: \ket{V_\alpha V_\beta}=\sin\alpha\sin\beta\ket{HH}-\sin\alpha\cos\beta\ket{HV}-\cos\alpha\sin\beta\ket{VH}+\cos\alpha\cos\beta\ket{VV}, with c_0=\frac{1-\sin2\theta\cos{\delta}\cos2\alpha}{4},c_1=\frac{\cos(2\alpha)-\cos\delta\sin2\theta}{4} and c_2=\frac{\cos2\theta\sin2\alpha}{4}. The incoming entangled photon pairs and background rates are indicated as N_0 and N_d respectively. Then the total coincidence can be modelled using the equation: N(\alpha,\beta)=N_0P_{VV}(\alpha,\beta)+N_d = C_0+C_1\cos(2\beta)+C_2\sin(2\beta), where C_0=-\frac{N_0\cos\delta\sin{2\theta}}{4}\cos{2\alpha}+\frac{N_0+4N_d}{4}, C_1=\frac{N_0}{4}\cos{2\alpha}-\frac{N_0\cos\delta\sin{2\theta}}{4} and C_2=\frac{N_0\cos{2\theta}}{4}\sin{2\alpha}. Experimentally, we will evaluate the rate of coincidences using two single-photon counting modules (or Tpx3 cameras with infra-red amplification), located in the QIST laboratory after propagation in the ESnet fiber loops and in the Garden City (or Stony Brook) measurement module, as a dependence on the polarization angles \alpha and \beta, which will be set by synchronizing the rotation of two polarizers at the remote locations. The coincidence data for different settings of the polarizers will then be used to calculate the Clauser-Horne-Shimony-Holt (CHSH) inequality violation \cite{Ianzano2018}. The inequality can be written as: S=E(\alpha,\beta)+E(\alpha',\beta)-E(\alpha,\beta')+E(\alpha',\beta')\le 2, where E(\alpha,\beta)=\frac{N_{VV}(\alpha,\beta)+N_{HH}(\alpha,\beta)-N_{VH}(\alpha,\beta)-N_{HV}(\alpha,\beta)}{N_{VV}(\alpha,\beta)+N_{HH}(\alpha,\beta)+N_{VH}(\alpha,\beta)+N_{HV}(\alpha,\beta)}. Measurement of a S value > 2 will signal the successful distribution of entanglement.

Polarization compensation and synchronization. In this entanglement distribution scenario, the fibers between the measurement stations and the source are long and propagate through telecom infrastructure. This can cause significant fluctuations in the power and drifts in polarization throughout propagation. Thus, for Bell-state entanglement verification measurements, the polarization axes have to be corrected at the two receiving end-station. To mitigate these effects and ensure a BSM measurement in the proper basis, feedback on the polarization changes through propagation needs to be implemented in near real-time. This will be done by coupling another near-wavelength light field of known fixed polarization and compensating electro-optically with fast feedback-loops before the measurement station.

Coexistence experiments. Distributing entanglement over a long distance fiber requires the exchange of classical signals in order to synchronize the clocks and correct the polarization axes before the characterization measurements in the remote locations. As explained above, one of the possible options to achieve this synchronization is the use of a fiber time-base distribution system (e.g., White Rabbit) to exchange pulsed clock information to assign time tags in remote detectors within the same <50ns temporal frame. The synchronization pulses travel in fibers at wavelengths of 1310 and 1550nm. These long distance experiments are also a good test-bed to benchmark the co-existence of classical information (synchronization pulses) and quantum information (entanglement) in a single fiber. Experiments will be developed in which both the entanglement at 1324nm or 1367nm rubidium wavelength and the timing pulses at 1550nm will be coupled into the same fiber going to the Garden City colocation facility. Once there, wavelength filters will separate the signals.

Network architecture and physical link layer design. An important part of the development of the quantum repeater network is to visualize and implement the physical and link layer protocols that will convert the physics experiments distributing quantum entanglement described above, into well-defined networking services. In this part of the proposal we will design protocols that permit the software control of the quantum network.

The task of this envisioned link layer will be to turn the physical layer composed of qubit generators, entanglement sources, quantum memories and measurement stations (communicating through optical fiber using the quantum-memory compatible 1324, 1367 and 1552 nm wavelengths), into an entanglement generation service. This service should be designed to produce entanglement between controllable quantum nodes (quantum memories) connected by a chain of automated quantum nodes (entanglement and qubit sources).

Requests can be made by higher layers to the link layer to produce entanglement using the standard Dense-Wave-Division-Multiplexing (DWDM) telecom wavelengths. The robustness of the network can be guaranteed by instructing the physical layer to perform many attempts to produce entanglement until success or result in a time-out.

Quantum repeater physical link layer. Control signals encoded in the DWDM telecom C-band are sent to the physical elements of the quantum repeater network. Quantum light signals (carrying qubits and entanglement) are encoded in the O-band, in the quantum memory-compatible wavelength of 1324 and 1367 nm (an additional memory-compatible wavelength of 1552 nm can be accommodated within a standard C-band channel). These signals can be multiplexed to travel and co-exist in the same optical fiber. De-multiplexing allows for amplification of the classical control signals, independently from the quantum information. The classical signals can be then sent to remote locations in the network to control the local aspects of quantum devices. The quantum signals are sent to quantum memories for synchronization, and entanglement swapping operations.

Propagation of CV squeezing over long distances. As mentioned above, the entanglement source can be easily converted into a CV squeezed light source by exchanging the non-linear crystals. Using the frequency conversion units, squeezed light at telecom wavelengths can be created and the survival of quantum noise reduction can be evaluated versus the propagation distance. The ESnet loops at BNL are an appropriate test-bed for such characterization. The evaluation of the squeezing degree will be performed using a homodyne detector located in the SDCC facility.

Deliverable of Thrust II: Distribution of telecom entanglement over long distance fibers over Long Island}. A portable high repetition rate entangled source compatible with atomic lines will be frequency converted to telecom using two room temperature quantum light matter interfaces in BNL. The telecom entanglement compatible with rubidium transitions will be distributed using long distance fiber networks to the Stony Brook campus or the Garden City colocation facility.

Metrics of success: We expect to achieve efficiencies of frequency conversion at the single photon level > 40%, reproducing the state of the art. Having developed successful synchronization and polarization compensation techniques will allow us to measure violation of Bell’s inequalities with telecom entangled photons over distances close to 200 km. We further expect to successfully multiplex-demultiplex quantum and classical optical signals on the same fiber and prove that co-existence is possible with the quantum channel sustaining minimal losses.