Quantum Optics of Spin Waves through ac Stark Modulation

Michał Parniak, Mateusz Mazelanik, Adam Leszczyński, Michał Lipka, Michał Dąbrowski, and Wojciech Wasilewski

Phys. Rev. Lett. 122, 063604 – Published 14 February 2019

Abstract

We bring the set of linear quantum operations, important for many fundamental studies in photonic systems, to the material domain of collective excitations known as spin waves. Using the ac Stark effect we realize quantum operations on single excitations and demonstrate a spin-wave analog of the Hong-Ou-Mandel effect, realized via a beam splitter implemented in the spin-wave domain. Our scheme equips atomic-ensemble-based quantum repeaters with quantum information processing capability and can be readily brought to other physical systems, such as doped crystals or room-temperature atomic ensembles.

Received 10 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.063604

Physics Subject Headings (PhySH)

Collective effects in quantum optics Photon pairs & parametric down-conversion Photon statistics Quantum information with atoms & light Quantum memories Quantum state engineering Quantum states of light

Atomic ensemble

Holography Optical interferometry Photon counting

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Michał Parniak^1,2,*, Mateusz Mazelanik^1,2,†, Adam Leszczyński^1,2, Michał Lipka^1,2, Michał Dąbrowski^1,2, and Wojciech Wasilewski^1,2

¹Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
²Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland

^*michal.parniak@fuw.edu.pl
^†mateusz.mazelanik@fuw.edu.pl

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Vol. 122, Iss. 6 — 15 February 2019

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Images

Figure 1
Experimental setup for generating and manipulating SWs. (a) Detection of a single write-out photon $w$ scattered from write laser $W$ heralds creation of a SW inside the atomic ensemble. The SW is then manipulated using an ACS light pattern (d) generated with a far-detuned laser $S$ . The SW can then be converted by the read laser $R$ to a readout photon $r$ with a reshaped spatial mode. (c) The relevant energy level configuration: $| g ⟩ = | 5^{2} S_{1 / 2} F = 1, m_{F} = 1 ⟩$ and $| h ⟩ = | 5^{2} S_{1 / 2} F = 2, m_{F} = - 1 ⟩$ . The write laser is red detuned from the $5^{2} S_{1 / 2} F = 1 \to 5^{2} P_{3 / 2} F = 2$ transition by 25 MHz, the read laser is resonant with the $5^{2} S_{1 / 2} F = 2 \to 5^{2} P_{1 / 2} F = 2$ transition, and the ACS laser $S$ is red detuned from the $5^{2} S_{1 / 2} F = 2 \to 5^{2} P_{3 / 2}$ line centroid by 1.43 GHz. During QM operation we keep constant bias magnetic field $B = (50 mG) {\hat{e}}_{z}$ . (b) The sequence revealing the timing of each step during the experiment.
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Figure 2
Performance of the SW phase modulator. (a) Light intensity emitted from a SW as a function of a pure sine modulation rms amplitude $\sqrt{⟨ φ_{S}^{2} ⟩}$ and the wave vector $K_{y}$ component; (b) intensities in diffraction orders 0–2, marked in (a) along with the expected behavior (lines). In (c),(d) we change the modulation to include a term with higher frequency (insets: phase modulation patterns). Depending on the relative phase between the two terms, we observe diffraction predominantly in the selected direction.
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Figure 3
A reference measurement (a) of second-order cross-correlation $g_{r w}^{(2)}$ reveals a single peak at $k_{y}^{r} + k_{y}^{w} = 0$ , demonstrating momentum anticorrelations. By reshaping the SWs with a sine modulation pattern with wave vector $k_{g}$ , we modify the correlation function (b) to feature two additional peaks at $k_{y}^{r} + k_{y}^{w} = \pm k_{g}$ .
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Figure 4
The protocol for quantum interference of SWs. Detection of two $w$ photons in modes $w a$ and $w b$ (selected through single-mode fibers) heralds generation of a SW pair in modes $r a$ and $r b$ . The three-way splitter is then used to interfere the two SWs. By detecting the SWs through photons converted to $r c$ and $r d$ modes, we observe bunching due to their bosonic nature. Inset (i) presents the input SW modes in the ( $K_{x}$ , $K_{y}$ ) plane. Photonic detection modes are always set to collect photons emitted from heralded SW modes.
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Figure 5
Demonstration of quantum interference of SWs. (a) HOM dip as a function of mode wave vector separation. Bunching may be suppressed if the modes $r a$ and $r b$ are separated in the $K_{x}$ direction of the momentum space. (b) By heralding only the $w$ photon in the $w a$ mode, we implement a HBT experiment, observing nonclassical statistics of the SW state. (c) The second-order correlation between $w$ and $r$ photons validating the operation of the three-way splitter with a slight drop in $g_{w a, r c}^{(2)}$ due to residual misalignment as the modes are moved (resulting in reduced fiber coupling efficiency). (d) HOM experiment for coherent input state with phase averaging. Vertical error bars correspond to one standard deviation inferred from Poissonian statistics of photon counts; horizontal error bars are due to mechanical precision of mode selection.
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