Abstract

Plenty of quantum information protocols are enabled by manipulation and detection of photonic spectro-temporal degrees of freedom via light–matter interfaces. While present implementations are well suited for high-bandwidth photon sources such as quantum dots, they lack the high resolution required for intrinsically narrowband light–atom interactions. Here, we demonstrate far-field temporal imaging based on ac-Stark spatial spin-wave phase manipulation in a multimode gradient echo memory. We achieve a spectral resolution of 20 kHz with MHz-level bandwidth and an ultralow noise equivalent to 0.023 photons, enabling operation in the single-quantum regime.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2020 (1)

Y. Mei, Y. Zhou, S. Zhang, J. Li, K. Liao, H. Yan, S.-L. Zhu, and S. Du, “Einstein–Podolsky–Rosen energy-time entanglement of narrowband biphotons,” Phys. Rev. Lett. 124, 010509 (2020).
[Crossref]

2019 (8)

H. Babashah, Z. Kavehvash, A. Khavasi, and S. Koohi, “Temporal analog optical computing using an on-chip fully reconfigurable photonic signal processor,” Opt. Laser Technol. 111, 66–74 (2019).
[Crossref]

M. Parniak, M. Mazelanik, A. Leszczyński, M. Lipka, M. Dąbrowski, and W. Wasilewski, “Quantum optics of spin waves through ac stark modulation,” Phys. Rev. Lett. 122, 063604 (2019).
[Crossref]

M. Lipka, A. Leszczyński, M. Mazelanik, M. Parniak, and W. Wasilewski, “Spatial spin-wave modulator for quantum-memory-assisted adaptive measurements,” Phys. Rev. Appl. 11, 034049 (2019).
[Crossref]

H. Jeong, S. Du, and N. Y. Kim, “Proposed narrowband biphoton generation from an ensemble of solid-state quantum emitters,” J. Opt. Soc. Am. B 36, 646 (2019).
[Crossref]

H.-H. Lu, J. M. Lukens, B. P. Williams, P. Imany, N. A. Peters, A. M. Weiner, and P. Lougovski, “A controlled-NOT gate for frequency-bin qubits,” npj Quantum Inf. 5, 24 (2019).
[Crossref]

M. Mazelanik, M. Parniak, A. Leszczyński, M. Lipka, and W. Wasilewski, “Coherent spin-wave processor of stored optical pulses,” npj Quantum Inf. 5, 22 (2019).
[Crossref]

A. Seri, D. Lago-Rivera, A. Lenhard, G. Corrielli, R. Osellame, M. Mazzera, and H. de Riedmatten, “Quantum storage of frequency-multiplexed heralded single photons,” Phys. Rev. Lett. 123, 080502 (2019).
[Crossref]

H. Wu, P. Ryczkowski, A. T. Friberg, J. M. Dudley, and G. Genty, “Temporal ghost imaging using wavelength conversion and two-color detection,” Optica 6, 902 (2019).
[Crossref]

2018 (4)

H. H. Lu, J. M. Lukens, N. A. Peters, O. D. Odele, D. E. Leaird, A. M. Weiner, and P. Lougovski, “Electro-optic frequency beam splitters and tritters for high-fidelity photonic quantum information processing,” Phys. Rev. Lett. 120, 030502 (2018).
[Crossref]

G. Patera, D. B. Horoshko, and M. I. Kolobov, “Space-time duality and quantum temporal imaging,” Phys. Rev. A 98, 053815 (2018).
[Crossref]

E. Saglamyurek, T. Hrushevskyi, A. Rastogi, K. Heshami, and L. J. LeBlanc, “Coherent storage and manipulation of broadband photons via dynamically controlled Autler–Townes splitting,” Nat. Photonics 12, 774–782 (2018).
[Crossref]

A. Leszczyński, M. Mazelanik, M. Lipka, M. Parniak, M. Dąbrowski, and W. Wasilewski, “Spatially resolved control of fictitious magnetic fields in a cold atomic ensemble,” Opt. Lett. 43, 1147 (2018).
[Crossref]

2017 (8)

M. Karpiński, M. Jachura, L. J. Wright, and B. J. Smith, “Bandwidth manipulation of quantum light by an electro-optic time lens,” Nat. Photonics 11, 53–57 (2017).
[Crossref]

Y. F. Pu, N. Jiang, W. Chang, H. X. Yang, C. Li, and L. M. Duan, “Experimental realization of a multiplexed quantum memory with 225 individually accessible memory cells,” Nat. Commun. 8, 15359 (2017).
[Crossref]

M. Parniak, M. Dąbrowski, M. Mazelanik, A. Leszczyński, M. Lipka, and W. Wasilewski, “Wavevector multiplexed atomic quantum memory via spatially-resolved single-photon detection,” Nat. Commun. 8, 2140 (2017).
[Crossref]

S. Denis, P. A. Moreau, F. Devaux, and E. Lantz, “Temporal ghost imaging with twin photons,” J. Opt. 19, 34002 (2017).
[Crossref]

M. Allgaier, V. Ansari, L. Sansoni, C. Eigner, V. Quiring, R. Ricken, G. Harder, B. Brecht, and C. Silberhorn, “Highly efficient frequency conversion with bandwidth compression of quantum light,” Nat. Commun. 8, 14288 (2017).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Magnified time-domain ghost imaging,” APL Photon. 2, 46102 (2017).
[Crossref]

X. Guo, Y. Mei, and S. Du, “Testing the Bell inequality on frequency-bin entangled photon pairs using time-resolved detection,” Optica 4, 388 (2017).
[Crossref]

S. Hong, R. Riedinger, I. Marinković, A. Wallucks, S. G. Hofer, R. A. Norte, M. Aspelmeyer, and S. Gröblacher, “Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator,” Science 358, 203–206 (2017).
[Crossref]

2016 (7)

P. Farrera, G. Heinze, B. Albrecht, M. Ho, M. Chávez, C. Teo, N. Sangouard, and H. De Riedmatten, “Generation of single photons with highly tunable wave shape from a cold atomic ensemble,” Nat. Commun. 7, 13556 (2016).
[Crossref]

J. M. Donohue, M. Mastrovich, and K. J. Resch, “Spectrally engineering photonic entanglement with a time lens,” Phys. Rev. Lett. 117, 243602 (2016).
[Crossref]

S. Dong, W. Zhang, Y. Huang, and J. Peng, “Long-distance temporal quantum ghost imaging over optical fibers,” Sci. Rep. 6, 26022 (2016).
[Crossref]

Y.-W. Cho, G. T. Campbell, J. L. Everett, J. Bernu, D. B. Higginbottom, M. T. Cao, J. Geng, N. P. Robins, P. K. Lam, and B. C. Buchler, “Highly efficient optical quantum memory with long coherence time in cold atoms,” Optica 3, 100–107 (2016).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

P. Suret, R. El Koussaifi, A. Tikan, C. Evain, S. Randoux, C. Szwaj, and S. Bielawski, “Single-shot observation of optical rogue waves in integrable turbulence using time microscopy,” Nat. Commun. 7, 13136 (2016).
[Crossref]

M. Rambach, A. Nikolova, T. J. Weinhold, and A. G. White, “Sub-megahertz linewidth single photon source,” APL Photon. 1, 096101 (2016).
[Crossref]

2015 (2)

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).
[Crossref]

B. Li, M. R. Fernández-Ruiz, S. Lou, and J. Azaña, “High-contrast linear optical pulse compression using a temporal hologram,” Opt. Express 23, 6833 (2015).
[Crossref]

2014 (2)

L. Zhao, X. Guo, C. Liu, Y. Sun, M. M. T. Loy, and S. Du, “Photon pairs with coherence time exceeding 1 µs,” Optica 1, 84 (2014).
[Crossref]

P. C. Humphreys, W. S. Kolthammer, J. Nunn, M. Barbieri, A. Datta, and I. A. Walmsley, “Continuous-variable quantum computing in optical time-frequency modes using quantum memories,” Phys. Rev. Lett. 113, 130502 (2014).
[Crossref]

2013 (3)

Y. Zhu, J. Kim, and D. J. Gauthier, “Aberration-corrected quantum temporal imaging system,” Phys. Rev. A 87, 43808 (2013).
[Crossref]

V. J. Hernandez, C. V. Bennett, B. D. Moran, A. D. Drobshoff, D. Chang, C. Langrock, M. M. Fejer, and M. Ibsen, “104  MHz rate single-shot recording with subpicosecond resolution using temporal imaging,” Opt. Express 21, 196–203 (2013).
[Crossref]

B. M. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. P. Robins, and B. C. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15, 085027 (2013).
[Crossref]

2012 (3)

X. H. Bao, A. Reingruber, P. Dietrich, J. Rui, A. Dück, T. Strassel, L. Li, N. L. Liu, B. Zhao, and J. W. Pan, “Efficient and long-lived quantum memory with cold atoms inside a ring cavity,” Nat. Phys. 8, 517–521 (2012).
[Crossref]

A. Stute, B. Casabone, P. Schindler, T. Monz, P. O. Schmidt, B. Brandstätter, T. E. Northup, and R. Blatt, “Tunable ion-photon entanglement in an optical cavity,” Nature 485, 482–485 (2012).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

2010 (1)

M. P. Hedges, J. J. Longdell, Y. Li, and M. J. Sellars, “Efficient quantum memory for light,” Nature 465, 1052–1056 (2010).
[Crossref]

2009 (5)

2008 (1)

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[Crossref]

2004 (1)

2001 (1)

C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron. 37, 20–32 (2001).
[Crossref]

2000 (1)

L. K. Mouradian, F. Louradour, V. Messager, A. Barthélémy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795–801 (2000).
[Crossref]

1999 (1)

1994 (2)

C. V. Bennett, R. P. Scott, and B. H. Kolner, “Temporal magnification and reversal of 100  Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[Crossref]

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270–272 (1994).
[Crossref]

1989 (2)

B. H. Kolner and M. Nazarathy, “Temporal imaging with a time lens,” Opt. Lett. 14, 630 (1989).
[Crossref]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[Crossref]

1988 (1)

B. H. Kolner, “Active pulse compression using an integrated electro-optic phase modulator,” Appl. Phys. Lett. 52, 1122–1124 (1988).
[Crossref]

1974 (1)

D. Grischkowsky, “Optical pulse compression,” Appl. Phys. Lett. 25, 566–568 (1974).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[Crossref]

Albrecht, B.

P. Farrera, G. Heinze, B. Albrecht, M. Ho, M. Chávez, C. Teo, N. Sangouard, and H. De Riedmatten, “Generation of single photons with highly tunable wave shape from a cold atomic ensemble,” Nat. Commun. 7, 13556 (2016).
[Crossref]

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[Crossref]

Allgaier, M.

M. Allgaier, V. Ansari, L. Sansoni, C. Eigner, V. Quiring, R. Ricken, G. Harder, B. Brecht, and C. Silberhorn, “Highly efficient frequency conversion with bandwidth compression of quantum light,” Nat. Commun. 8, 14288 (2017).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Temporal imaging state of the art, characterized by temporal $ \delta t $ and spectral $ \delta \omega $ resolutions. Numerous implementations based on solid media (electro-optic modulators or EOMs [25,4345]; four-wave mixing, or FWM [24,46]; sum-frequency generation, or SFG [20,47]; and cross-phase modulation, or XPM [48]) are well suited for high bandwidth pico- or even femtosecond pulses, achieving spectral resolution no better than 1 GHz, with time-bandwidth products ($ \tau {\cal B} $) reaching $ 2\pi \times 2000 $. Our system–GEM & SSM–has $ {10^6} $ times better spectral resolution $ \delta \omega /2\pi \sim 20\;{\rm kHz} $, maintaining good $ \tau {\cal B} $, thus allowing exploration of a previously unattainable region. The grayed region indicates an unphysical area bounded by the Fourier limit $ \tau {\cal B}/2\pi = 1 $.
Fig. 2.
Fig. 2. (a) Light–atom interface. Chirped control field simultaneously allows mapping of the signal optical field onto the atomic coherence $ {\rho _{hg}} $ and realizes the temporal lens. (b) Projection of signal spectral components onto atomic coherence spatial components in GEM with Zeeman splitting gradient $ \beta $. (c) During the writing process atoms are placed in a negative magnetic field gradient along the cloud (${w}$). When the writing finishes, the spatial phase of the atomic coherence is modulated with a parabolic Fresnel profile that realizes a temporal equivalent of free-space propagation. Finally, the gradient is switched to positive (${r}$) and the coherence is converted back to light, which is further registered with single photon counting module (SPCM) connected to the time tagger (TTG). (d) Evolution of the spectro-temporal Wigner function on subsequent stages of far-field temporal imaging: (1) time lens, (2) free-space propagation, and (3) time lens. The complete transformation effectively rotates the initial Wigner function of two pulses (equivalent to a Wigner function of a cat state in phase space) by $ \pi /2 $, as given by Eq. (1).
Fig. 3.
Fig. 3. Experimental sequence for temporal imaging. (a) Time-trace of the Zeeman shift gradient $ \beta $ used in the GEM protocol, allowing two-directional mapping of signal frequencies to distinct positions in the atomic cloud. (b) Control field (red) and SSM (yellow) laser pulse sequence divided into three stages corresponding to lens–propagation–lens operations. The lens (1) is implemented during the GEM writing process by a chirped control field. (2) The 3 µs long SSM laser pulse imprints a parabolic phase profile onto the stored atomic coherence, which realizes the spectro-temporal free-space propagation. During this stage, the magnetic field gradient is reversed, allowing remapping the coherence to light. (3) Finally, the control field is turned on and the coherence is read out from the memory. Chirping the control field would implement the second lens. However, for simplicity, the control field is no longer chirped as the imposed phase would not be registered by the SPCM. (c, e) Example results for two pulses or a sine wave as inputs, respectively. Gray bins represent single photon counts. Red line corresponds to the numerical simulations. (d, f) Normalized modulus square of atomic coherence in Fourier space. The insets (i, ii) show experimentally obtained linear dependency of the time delay $ \Delta t $ (in $\unicode{x00B5}{\rm s} $) on the signal modulation frequency $ f $ (in MHz) defined on panels (c, e).
Fig. 4.
Fig. 4. Characterization and tuning of bandwidth and resolution. (a) Efficiency spectral profile $ {\eta _0}(\omega ) $ as a function of the two-photon detuning $ \delta = \omega - {\omega _0} $ for a chosen time-bandwidth product $ \tau {\cal B} = 2\pi \times 13 $ with bandwidth $ {\cal B} $ defined as the FWHM of $ {\eta _0}(\omega ) $. The red line corresponds to a super-Gaussian approximation of the atom concentration used in the simulation. (b) Dependence of the bandwidth $ {\cal B} $ as a function of the Zeeman splitting gradient $ \beta $. Red line is a linear fit to the data. (c) Time evolution of the GEM efficiency due to incoherent scattering caused by the coupling field. The characteristic decay time $ \tau $ obtained from exponential fit (red line) limits the effective resolution $ \delta \omega /2\pi = 0.78/\tau $ (here $ \tau = 10\;\unicode{x00B5} {\rm s} $). (d) Dependence of $ 1/\tau $ as a function of the coupling field power $ P \propto |\Omega {|^2} $, along with linear fit (red line). (e) Calculated map of the average efficiency $ \bar \eta $ for varying bandwidth $ {\cal B} $ and decay time $ \tau $. The efficiency for a given time-bandwidth product $ \tau {\cal B} $ is approximately constant as expected. The star indicates the point of operation where the exemplary measurements (Fig. 3) were performed.

Equations (3)

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$$\begin{split}\left[ {\begin{array}{*{20}{c}}{t^{\prime}}\\{\frac{{\omega^{\prime}}}{{{\omega _0}}}}\end{array}} \right] &= \left[ {\begin{array}{*{20}{c}}1&0\\{ - \frac{1}{{{f_{\rm t}}}}}&1\end{array}} \right]\left[ {\begin{array}{*{20}{c}}1&{{f_{\rm t}}}\\0&1\end{array}} \right]\left[ {\begin{array}{*{20}{c}}1&0\\{ - \frac{1}{{{f_{\rm t}}}}}&1\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{t}\\{\frac{\omega }{{{\omega _0}}}}\end{array}} \right]\\& = \left[ {\begin{array}{*{20}{c}}0&{{f_{\rm t}}}\\{ - \frac{1}{{{f_{\rm t}}}}}&0\end{array}} \right]\left[ {\begin{array}{*{20}{c}}{t}\\{\frac{\omega }{{{\omega _0}}}}\end{array}} \right],\end{split}$$
$${\eta _0} = {\left[ {1 - \exp \left( { - 2\pi \frac{{{\rm OD}}}{{\tau {\cal B}}}} \right)} \right]^2},$$
$$\begin{split}\bar \eta &= \frac{1}{{2\tau {\cal B}}}\int_{ - {\cal B}/2}^{{\cal B}/2} \int_0^{2\tau } \eta (t,\omega ){\rm d}t{\rm d}\omega\\& = \frac{{{e^2} - 1}}{{2{e^2}{\cal B}}}\int_{ - {\cal B}/2}^{{\cal B}/2} {\eta _0}(\omega ){\rm d}{\omega}.\end{split}$$

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