Few-Mode-Fiber Technology Fine-tunes Losses in Quantum Communication Systems

A natural choice for quantum communication is to use the relative phase between two paths of a single photon for information encoding. This method was nevertheless quickly identified as impractical over long distances, and thus a modification based on single-photon time bins has become widely adopted. It, however, introduces a fundamental loss, which increases with the dimension and limits its application over long distances. Here solve this long-standing hurdle by using a few-mode-fiber space-division-multiplexing platform working with orbital-angular-momentum modes. In our scheme, we maintain the practicability provided by the time-bin scheme, while the quantum states are transmitted through a few-mode fiber in a configuration that does not introduce postselection losses. We experimentally demonstrate our proposal by successfully transmitting phase-encoded single-photon states for quantum cryptography over 500 m of few-mode fiber, showing the feasibility of our scheme.

Figure 1

Phase-coding quantum cryptography. (a) Original scheme based on a long Mach-Zehnder interferometer that must be phase stabilized. Phase modulators are used to prepare and measure the required states. The inset shows that photons transmitted through paths $|0⟩$ and $|1⟩$ will arrive in the same detection time window. (b) Typical time-bin-based scheme, relying on a single fiber interconnecting two asymmetrical short interferometers (easier to stabilize). Temporal postselection is required. Photons will arrive in three different time bins (see the inset). To extract a secret key, the ones arriving too early or too late must be discarded, thus drastically reducing the communication rate by 50%. (c) Our setup resorting to few-mode-fiber technology. It borrows concepts of the robust time-bin configuration: two short interferometers interconnected through a single (few-mode) fiber. Photons traveling through paths $|0⟩$ and $|1⟩$ are mapped to orthogonal optical modes supported by the fiber using a photonic lantern, and are demultiplexed in an inverse fashion by another lantern. Since the local interferometers are now symmetrical, these photons will again arrive in the same time bin and no temporal postselection is needed. D, detector; FC, fiber coupler; SPS, single-photon source.

Figure 2

Spatial intensity profiles of the output of the FMF as measured by an ($\mathrm{In}$,$\mathrm{Ga}$)$\mathrm{As}$ CCD camera. (a) Theoretical spatial profiles of the ${\mathrm{LP}}_{11a}$ and ${\mathrm{LP}}_{11b}$ modes and experimental results in the back-to-back case and after an extra 500 m of FMF. (b),(c) Theoretical and experimental spatial profiles (back-to-back case and after 500-m of propagation) associated with the $|{\mathrm{LP}}_{\pm }⟩$ and $|{\mathrm{OAM}}_{\pm }⟩$ states, respectively.

Figure 3

Single-photon interference curves after 500 m of propagation over the few-mode fiber. The relative phase $({\varphi }_A)$ is modulated with a slow-driving triangular signal. (a) Interference curves recorded while the detection stage is set for measuring at the first mutually unbiased base defined by ${\varphi }_B=0$. (b) Interference curves recorded while the detection stage is set for measuring at the second mutually unbiased base defined by ${\varphi }_B=\pi /2$. The standard deviation is calculated assuming Poissonian statistics. The deviation of the experimental data from the theoretical fit is due to the residual phase drift present acting on Alice and Bob's local interferometers, which are not actively phase stabilized. D, detector.

Figure 4

Probabilities associated with the states of the BB84 quantum cryptography protocol. The vertical axis show the states being prepared, while the horizontal axis shows onto which state the projection is made. (a) The probabilities in the back-to-back case and (b) the same probabilities following 500 m of propagation over the FMF. See the main text for details.

Figure 5

Qudit-based quantum communication scheme using phase encoding with few-mode fibers. D, detector; FC, fiber coupler; SPS, single-photon source.

Figure 6

Fourier spectra of 50 min-long measurements of the interferometer output, when the input state is continuously modulated with a 100-Hz sinusoidal wave, for both the back-to-back case (a) and after an extra 500 m of FMF (b).