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Multiplexed storage and real-time manipulation based on a multiple-degree-of-freedom quantum memory
Tian-Shu Yang, Zong-Quan Zhou, Yi-Lin Hua, Xiao Liu, Zong-Feng Li, Pei-Yun Li, Yu Ma, Chao Liu, Peng-Jun Liang, Xue Li, Yi-Xin Xiao, Jun Hu, Chuan-Feng Li, Guang-Can Guo
TL;DR
Multiplexed quantum repeaters require memories that can store photons across multiple modes, while prior memory experiments had mostly used a single degree of freedom at a time. This work demonstrates a solid-state memory that stores OAM qutrits while multiplexing temporal, spectral, and spatial modes, and converts temporal and spectral modes in real time while preserving qutrit properties.
Problem
Most previous quantum-memory experiments stored multiple modes using only one degree of freedom, limiting the demonstrated combination of modes relevant to multiplexed quantum repeaters.
Source: Introduction · p. 1Method
The authors demonstrate on-demand spin-wave storage of OAM qutrits in a rare-earth-ion crystal, multiplexing spatial modes with temporal and spectral modes and using memory control for real-time mode conversion.
Source: Introduction · p. 1, Experimental Setup · p. 2, Multiplexing storage in multiple DOF · p. 4Results
0.909 ± 0.010 fidelity to Identity operation exceeded the classical bound of 0.831; the memory also converted arbitrary temporal and spectral modes in real time while preserving spatial-qutrit quantum properties.
Source: Quantum process tomography · p. 3, Multiplexing storage in multiple DOF · p. 4Takeaways & Limitations
The authors state that the device can perform arbitrary single-qubit operations through temporal and spectral manipulation of photonic pulses.
Source: Discussion · p. 5Spatial-domain mode conversion was not demonstrated in this work, although the authors state it should be feasible using a high-speed digital micro-mirror device.
Source: Discussion · p. 5
Abstract
from arXiv · showhide
The faithful storage and coherent manipulation of quantum states with matter-systems enable the construction of large-scale quantum networks based on quantum repeater. To achieve useful communication rates, highly multimode quantum memories will be required to construct a multiplexed quantum repeater. Here, we present the first demonstration of the on-demand storage of orbital-angular-momentum states with weak coherent pulses at the single-photon-level in a rare-earth-ion doped crystal. Through the combination of this spatial degree-of-freedom with temporal and spectral degrees of freedom, we create a multiple-degree-of-freedom memory with high multimode capacity. This device can serve as a quantum mode converter with high fidelity, which is the fundamental requirements for the construction of a multiplexed quantum repeater. This device further enables essentially arbitrary spectral and temporal manipulations of spatial-qutrit-encoded photonic pulses in real-time. Therefore, the developed quantum memory can serve as a building block for scalable photonic quantum information processing architectures.
Introduction
Quantum repeaters are proposed to extend optical-fiber communication beyond its current distance limits, and multiplexed memories are identified as a route to practical data rates. This work combines temporal, spectral, and spatial degrees of freedom in an on-demand memory for three-dimensional OAM states.
Introduction
- Multiplexed quantum memories are identified as the most significant route to practical data rates for quantum-repeater communication, which addresses fiber communication's distance limits.The introduction attributes those limits to exponential photon loss in optical fibers.Source: Introduction · p. 1
- Rare-earth-ion-doped crystals offer multiple-degree-of-freedom memories through their large inhomogeneous bandwidths and long coherence times at cryogenic temperatures.Prior demonstrations cited include 100 temporal modes, tens of on-demand temporal modes, and 26 frequency modes.Source: Introduction · p. 1
- The paper reports an on-demand rare-earth-ion-crystal memory for single photons encoded in three-dimensional OAM states, multiplexed simultaneously across temporal, spectral, and spatial degrees of freedom.It also describes a quantum mode converter that manipulates temporal and spectral modes independently and simultaneously.Source: Introduction · p. 1
Experimental Setup
The experiment uses a cryogenic Pr3+:Y2SiO5 spin-wave AFC memory with spatial, temporal, and spectral filtering. For Gaussian-mode inputs, it retrieves photons after 12.68 µs with a reported spin-wave efficiency of 5.51%.
Experimental Setup
- Spatial, temporal, and spectral filtering suppress noise, with the AOM gate blocking control pulses and two 2-nm bandpass filters at 606 nm suppressing fluorescence.The AOM gate also avoids burning a spectral hole in the filter crystal and blinding the single-photon detector.Source: Figure 1 · p. 2
- The Pr3+:Y2SiO5 memory and filter crystals are cooled to 3.2 K, and spin-wave AFC storage enables on-demand retrieval and extended storage time.The input and control beams enter in opposite directions with an approximately 4° angular offset to reject control light and free-induction-decay noise.Source: Experimental Setup · p. 2
- 5.51% spin-wave storage efficiency was measured for Gaussian-mode photons retrieved at 12.68 µs; the signal-to-noise ratio was approximately 39.7 ± 6.7 for input mean photon number µ = 1.12.The memory and filter crystals are 3 × 6 × 3 mm, 0.05%-doped crystals.Source: Experimental Setup · p. 2
Quantum process tomography
The authors use quantum process tomography to assess storage of OAM qutrits in a basis of Laguerre-Gaussian modes. The reconstructed process has fidelity above the stated classical bound, with nonuniform performance across the three spatial modes.
Quantum process tomography
- The qutrit basis uses Laguerre-Gaussian modes, with |L⟩, |G⟩, and |R⟩ denoting the OAM states used in the experiment.The modes are distinguished by azimuthal and radial indices.Source: Quantum process tomography · p. 2
- 0.909 ± 0.010 fidelity to Identity operation exceeded the classical bound of 0.831, confirming the quantum nature of the memory operation.The process matrix was reconstructed using quantum process tomography.Source: Quantum process tomography · pp. 2–3
- The authors attribute non-unity fidelity potentially to limited pump/control beam waist and imperfect overlap with different OAM modes; storage efficiency is balanced for symmetric modes but not all three considered modes.Superpositions of |L⟩ and |R⟩ performed better than the reported three-dimensional process fidelity.Source: Quantum process tomography · p. 3
Multiplexing storage in multiple DOF
The memory multiplexes spatial OAM modes together with temporal and spectral modes, and also converts temporal and spectral modes while preserving spatial-qutrit properties. The experiments demonstrate multiplexed storage and real-time quantum mode conversion.
Multiplexing storage in multiple DOF
- 2 × 2 × 3 = 12 modes are obtained by combining two temporal modes, two spectral modes, and three spatial OAM modes.The two AFCs are separated by 80 MHz; each has 200 kHz peak spacing and 2 MHz bandwidth. Their spin-wave efficiencies are 5.05% and 5.13%, respectively.Source: Multiplexing storage in multiple DOF · p. 3
- Approximately 15.2 was the reported minimum mode crosstalk for temporal and spectral multiplexing with spatial-qutrit encoding.Each temporal-spectral channel carries the state |ψ1⟩ = (|L⟩ + |G⟩ + |R⟩)/3.Source: Multiplexing storage in multiple DOF · p. 3
- The two-AOM gate can shift frequency, while control-pulse timing specifies on-demand recall time, enabling independent, simultaneous spectral and temporal mode conversion.The demonstrated conversions include fi to fj and ti to tj; the reported noise was significantly weaker than the converted signal.Source: Multiplexing storage in multiple DOF · pp. 3–4
- The quantum mode converter converted arbitrary temporal and spectral modes in real time while preserving the quantum properties of spatial-qutrit-encoded pulses.The authors connect the device to matching photon modes retrieved from different quantum memories.Source: Multiplexing storage in multiple DOF · p. 4
Arbitrary manipulations in real time
The memory performs temporal and spectral manipulations on OAM-qutrit pulses after absorption, including changes to retrieval time, frequency, and temporal splitting. The output states are characterized by quantum state tomography.
Arbitrary manipulations in real time
- The memory exchanges the retrieval times of f1 and f2 photons, retrieves both at t1, shifts f1 photons to f2, and temporally splits f1 while filtering f2.These four operations are demonstrated on the input state |ψ1⟩ encoded in f1t1 and f2t2 modes.Source: Arbitrary manipulations in real time · p. 5
- The four demonstrated operations include exchanging retrieval times, multiplexing photons at one retrieval time, selective frequency shifting, and configurable temporal beam splitting.The input state |ψ1⟩ is encoded in f1t1 and f2t2 modes.Source: Arbitrary manipulations in real time · p. 5
- For the |ψ2⟩ input encoded in f1t2 and f2t2, the selective shifter retrieves shifted f1 photons at t1 while f2 photons remain at t2.The output states were characterized by quantum state tomography, and Table 1 reports fidelities between output and input states.Source: Arbitrary manipulations in real time · p. 5
Discussion
The discussion presents the three-degree-of-freedom memory as a basis for multiplexed quantum mode conversion and outlines a possible route to much larger capacity. It also identifies potential network and photonic-processing uses, while noting that spatial mode conversion was not demonstrated.
Discussion
- Combining demonstrated and previously reported capacities could yield 60 × 50 × 51 = 153000 modes, which could greatly enhance data rates in memory-based quantum networks.The component capacities are more than 60 spectral modes, 50 temporal modes, and 51 OAM spatial modes.Source: Discussion · p. 5
- The memory operates simultaneously in three degrees of freedom and can serve as a quantum mode converter, a requirement for scalable networks based on multiplexed quantum repeaters.Spatial mode conversion was not demonstrated in this work, though the authors say it should be feasible using a high-speed digital micromirror device.Source: Discussion · p. 5
- The output mode |ψ⟩f1t1, f1t2 has slightly lower fidelity than the other outputs, attributed to fewer photon counts in each output.The table caption reports fidelities for qutrit states after temporal and spectral manipulations.Source: Table 1 · p. 5
- The discussion connects quantum mode conversion to correcting spectral or temporal mismatches between photons in networks with two quantum memories.It also identifies mode mismatch from fiber-loop length effects and photon-source time jitter as a possible boson-sampling application.Source: Discussion · p. 5
- Arbitrary temporal and spectral manipulations could provide a variable temporal beam splitter and relative phase shifter, enabling arbitrary single-qubit operations.The authors further propose that, combined with heralded single photons, the device should provide operations sufficient for universal quantum computing in the KLM scheme.Source: Discussion · p. 5
AFC preparation.
The AFC is prepared by tailoring the Pr3+ absorption spectrum with spectral hole burning, then using control pulses for spin-wave storage. The experiment's complete storage time was 12.68 µs.
AFC preparation.
- AFC preparation uses hole-burning pulses to create a spectral comb with periodicity Δ=200 kHz on the 1/2g-3/2e transition.Burn-back prepares a 2 MHz absorbing feature; clean pulses empty the 3/2g ground state, while the 5/2g state serves as an auxiliary state.Source: AFC preparation · pp. 5–6
- An AFC with periodicity Δ = 200 kHz maps signal photons and leads to an AFC echo after 1/Δ; two on-resonance control pulses induce reversible transfer involving the 3/2e state.Source: AFC preparation · p. 6
- 12.68 µs was the complete storage time, comprising 5 µs of AFC storage and 7.68 µs of spin-wave storage.The Fig. 4 caption describes multiplexed storage and quantum mode conversion for a spatially encoded qutrit using four temporal and spectral channels.Source: AFC preparation · p. 6, Figure 4 · p. 6
Filtering the noise.
The setup combines spatial, temporal, and spectral filtering to reduce noise. Its temporal gate blocks strong control pulses, while filters suppress fluorescence and isolate the spectral mode.
Filtering the noise.
- Spatial filtering uses an angular offset between oppositely directed input and control beams, while a two-AOM temporal gate blocks strong control pulses.Blocking the control pulses helps avoid burning a spectral hole in the filter crystal and blinding the single-photon detector.Source: Filtering the noise · p. 6
- Two 2-nm bandpass filters at 606 nm suppress incoherent fluorescence noise.Source: Filtering the noise · p. 6
- A narrow-band spectral filter in the filter crystal isolates the mode using a 0.8 MHz sweep, producing a transparent window of approximately 1.84 MHz.The filter crystal is double-pass configured to achieve high absorption.Source: Filtering the noise · p. 6
Quantum tomography.
The memory operation was characterized by quantum process tomography using nine linearly independent OAM qutrit inputs. Quantum state tomography reconstructed input and output density matrices for these states.
Quantum tomography.
- Nine linearly independent inputs—three OAM eigenstates and six superposition states—were chosen to reconstruct the process matrix χ.Source: Quantum tomography · p. 7
- The process matrix χ is expressed in the λi basis and maps an input density matrix ρin to an output density matrix ρout.Source: Quantum tomography · p. 7
- Input and output density matrices were reconstructed by quantum state tomography, using ρ=|ψ⟩⟨ψ| for a given qutrit state.Reconstructed density matrices for two OAM qutrit states are shown in Supplementary Note 3.Source: Quantum tomography · p. 8