Unconditional polarization qubit quantum memory at room temperature

Unconditional polarization qubit quantum memory at room temperature Mehdi Namazi,1 Connor Kupchak,1 Bertus Jordaan,1 Reihaneh Shahrokhshahi,1 and Eden Figueroa1

arXiv:1512.07374v1 [quant-ph] 23 Dec 2015

1

Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA Here we study how the optical response of cold atomic environments is transformed by the motion of atoms at room temperature and consequently characterize the optimal performance of room temperature quantum light-matter interfaces. Our findings enable us to attain complete quantum memory operation for polarization qubits in a warm 87 Rb atomic vapor with an average fidelity of 86.6 ± 0.6%, thereby defeating any classical strategy exploiting the non-unitary character of the memory efficiency. Our system significantly decreases the technological overhead required to achieve quantum memory operation and will serve as a building block for scalable and technologically simpler many-memory quantum machines.

Measuring quantum mechanical effects at room temperature is counter-intuitive due to inherent decoherence mechanisms. Nevertheless, robust and operational room temperature quantum devices are a fundamental cornerstone towards building quantum technology architectures consisting of multiple nodes [1, 2]. Given the recent success in the creation of elementary playgrounds in which single photons interact with atoms in controlled low temperature environments [3–6], the next technological frontier is the design of interfaces where such quantum mechanical processes can be performed at room temperature [7–11]. Optically-based quantum networks composed of a large number of quantum light sources and light-matter interfaces will be the basis of a diverse set of implementations, including the creation of quantum repeater networks [12], measurement device independent quantum cryptography links [13] and the analog quantum simulation of different physical platforms [14]. There exist cold atomic physical systems which have proven reliable for the transfer of the quantum properties from light to matter and viceversa [15]. Nevertheless, progressing these technologies to room temperature operation is key to unlock the potential and economical viability of novel multi-memory architectures [16–18]. In the past these systems have been labeled as unfavourable by the quantum information community since the fragile light states need to be transferred into collective atomic excitations that are impaired by strong atomic motion, decoherence and a considerable amount of background photons [19–27]. A pertinent metric of these effects is the signal-to-background ratio (SBR), defined as η/q, where η is the retrieved fraction of a single excitation stored in the medium and q the average number of concurrently emitted photons in a single retrieval event. Here we report that such once thought unsurmountable challenges can be bridged effectively using a complete understanding of the effects from motion and decoherence in an atomic-vapor-based light matter interface. The resultant optimization of the SBR allows us to demonstrate full quantum memory operation with polarization qubits in a dual rail system (see Fig. 1a). We

store 400 ns long pulses containing on average one qubit in warm 87 Rb vapor using electromagnetically induced transparency (EIT). Two independent control beams coherently prepare two volumes within a single 87 Rb vapor cell at 60◦ C, containing Kr buffer gas to serve as the storage medium for each mode of the polarization qubit. We employed two external-cavity diode lasers phase-locked at 6.835 GHz. The probe field frequency is stabilized to the 5S1/2 F = 1 → 5P1/2 F 0 = 1 transition at a wavelength of 795 nm (detuning ∆) while the control field interacts with the 5S1/2 F = 2 → 5P1/2 F 0 = 1 transition. Polarization elements supply 42 dB of control field attenuation (80% probe transmission) while two temperature-controlled etalon resonators (linewidths of 40 and 24 MHz) provide additional 102 dB of control field extinction. The total probe field transmission is 4.5% for all polarization inputs, exhibiting an effective, control/probe suppression ratio of 130 dB. First we will describe how the optical response of stationary atoms translates to that of atomic media at room temperature. We start by considering non-moving atoms exhibiting a four-level energy level scheme. The scheme is stimulated by the interaction with two laser fields, Ωp (probe) and Ωc (control), with one-photon detunings ∆13 and ∆23 respectively (see Fig. 1b) and includes the off-resonant interaction of the control field with a virtual state |4i. The phenomenological Hamiltonian which describes the atom-field coupling in a rotating frame is given by: ˆ = (−∆13 + ∆)ˆ H σ11 − (∆13 − ∆23 )ˆ σ22 α −Ωp Ep σ ˆ31 − Ωc Ec σ ˆ32 − Ωc Ec σ ˆ41 − ω43 + ∆ α Ωc Ec σ ˆ42 − (∆13 − ω43 )ˆ σ44 + h.c, ω43 + ∆ where ∆ is the laser detuning (scanning parameter), α is a fitting parameter describing the coupling strength to the virtual state, σ ˆij = |iihj|, i, j = 1, 2, 3, 4 are the atomic raising and lowering operators for i 6= j, and the atomic energy-level population operators for i = j and Ep (z, t) and Ec (z, t) are the normalized electric field amplitudes of the probe and control fields. We model the

2 5 2P 1/2

Control Laser

F=2 815MHz F=1

SPCM

87Rb-cell

w43

BD

Qubit

GLP

GLP

Polarization Filter

Dual-rail EIT Memory

0

795nm

BD

Spectral and Spatial Filters

Ωc

4

Ωp

F=2

Collective Atomic Spin Excitation

5 2 S1/2

1

Δ

Δ13 , Δ 23

Ωc

6.834GHz F=1

η (a. u.)

Transmission

FIG. 1. Experimental setup and atomic levels of the room temperature quantum memory. (a)Dual-rail quantum memory setup. Probe: red beam paths; control: yellow beam paths; BD: Polarization Beam Displacer; GLP: Glan Laser Polariser; SPCM: Single Photon Counter Module. The color-code bar depicts the strength of the collective atomic excitation. (b) Rubidium D1 line four-level scheme describing the transitions used in the description of the efficiency and background response. |1i and |2i (ground states), |3i (excited state), |4i (off-resonant virtual state) and ∆ (one-photon laser detuning).

1

F=1 to F’=1 F=1 to F’=2

ˆ ρˆ] + ρˆ˙ = −i[H,

0.5 0 0.4

Room Temperature Rb D1 line

+

X

Γ4m (2ˆ σm4 ρˆ σ4m − σ ˆ44 ρˆ − ρˆσ ˆ33 )

m=1,2

0 5 Efficiency ηD (%)

Γ3m (2ˆ σm3 ρˆ σ3m − σ ˆ33 ρˆ − ρˆσ ˆ33 )

m=1,2

0.2

4 3 2 1

0 −2000

X

−1000

0

∆(MHz)

1000

2000

FIG. 2. Room temperature storage efficiency response as a function of one photon detuning ∆. (a) Measured transmission profile TRT (∆). (b) Cold atom storage bandwidths η1 (∆) and η2 (∆) for the two excited states of the rubidium D1 line manifold (the blue line is a master equation prediction of the storage bandwidth) and room temperature storage bandwidth ηRT (∆) (the solid red line is the result of the convolution with a velocity distribution). (c) Overall efficiency response ∝ (ηRT (∆))(TRT (∆)) vs. one photon detuning ∆ (solid red line) and storage experiments over a 4 GHz scan region with a central frequency at the F = 1 to F 0 = 1 D1 line rubidium transition (blue dots). The error bars are statistical.

frequency response of the storage efficiency η(∆) in a cold atomic cloud by using the master equation:

together with the Maxwell-Bloch equation, ∂z Ep (z, t) = Ω N i pc hˆ σ31 (z, t)i, in an atomic sample of finite-length L where Γ’s being the decay rates of the excited levels, c is the speed of light in vacuum and N the number of atoms participating in the ensemble . By numerically solving this set of equations we can calculate the expected retrieved pulse shape EOU T (t) as a function of one-photon detuning, thus obtaining the storage efficiency bandwidth response of stationary atoms η(∆). We account for atomic motion and the cross influence of excited states by calculating a weighted average of two cold atom storage efficiency bandwidths η1 (∆) and η2 (∆) (corresponding to the two excited states of the rubidium D1 line manifold, blue line in Fig. 2b) and the distribution of possible atom velocities at a certain temperature. We use a Doppler distribution A(∆) = A(2πv/λ) = √ ln 1 √2 where Wd is the Doppler bandwidth Wd π 1+(2∆)2 /Wd2 and is set to be 960MHz, obtained from a fit on the measured transmission profile (Fig. 2a) to include also pressure broadening effects. The room temperature response is calculated by convolving the storage efficiency bandwidths η1 (∆) and η2 (∆) with A(∆). The detuning values were indexed such that ∆ = ∆j = ∆0 + j∆step and the Pimax response calculated η(∆j ) = i=−i A(∆i )η(∆j+i ). max The resultant broadened storage bandwidth ηRT (∆) is presented in Fig. 2b (solid red line). Finally we account for the varying optical depth at different ∆ frequencies by multiplying ηRT (∆) by the measured atomic transmission profile TRT (∆) (see Fig. 2a). The resultant is the room temperature efficiency bandwidth (see Fig. 2c red line). Using our dual √ rail scheme we perform storage experiments for (1/ 2|Hi + |V i) qubits with a storage time of

3 −3 1 x 10

0.8

Photons per pulse

0.6 0.4 0.2 0

−400

−200 0 200 Etalon Detuning (MHz)

1.3 x 10−3

400

F=1 to F’=2 F=1 to F’=1

1.1 0.9 0.7

3

SBR D

2 1 0 −2000

1000

0 ∆(MHz)

1000

2000

FIG. 3. Room temperature background response. (a) Cold atom background response Q(∆) (dashed red-line) featuring the contributions of incoherent scattering and Stokes fields; etalon transmission profile (dashed blue line); convoluted response indicating the background transmission through the filtering elements (solid blue line); experimental background measurement for ∆ = −500 MHz (green dots), 0 MHz (purple dots) and +500 MHz (black dots); technical background (brown dotted line). (b) Cold atom background bandwidths Q1 (∆) and Q2 (∆) for the two excited states of the rubidium D1 line manifold (the blue dotted line is a master equation prediction of the background bandwidth); warm atom background response QRT (∆) ((the solid red line is the result of the convolution with a velocity distribution)); background measurements vs. ∆ (blue dots). (c) Predicted room temperature signal to background ratio SBRRT ∝ (ηRT (∆))(TRT (∆))/(QRT (∆)) (solid red line); SBR experimental measurements (blue dots). The error bars are statistical.

700 ns over a ∆ region of 4 GHz. Figure 2c compares the results of our experiments to the prediction of our model. The most striking observation is that the maximum storage efficiency is not achieved when tuned on atomic resonance (as expected in a cold atomic system), but at detunings beyond the Doppler width of the resonance. These points correspond to detunings in which the EIT transmission overcomes maximally the on resonance absorption. The maximum efficiencies are at ∆ = 500 MHz

(red detuned) and ∆= 1.3 GHz (blue detuned). As a second step we simulate the quantum dynamics of the atomic system when no probe field is present. A time-varying control field excites coherences in the fourlevel atomic model and the time dependence of the photonic fields emitted is evaluated using several Liouvillian terms in the overall master equation. In order to simulate the contribution of the Stokes field in the memory background, we add an extra term to Ep (z, t) relative to hˆ σ42 (z, t)i. The numerical values used here are Γ3m = 3M Hz, Γ4m = 1GHz and the decoherence rate between ground states 0.1kHz. The cold atom background response Q(∆) is the combination of the fields created in the two coherences; first from transition |1i to |3i, which is narrow and associated to photons incoherently scattered from state |3i as a result of population exchange with the virtual state |4i, mediated by decoherence rates between the ground state |1i and |2i, and secondly, from the |2i to |4i transition, which is broad and associated to photons scattered from the virtual state |4i (Stokes field) through an off-resonant Raman process (see dotted red line if Fig. 3a) [25, 28]. These two fields are 13.6 GHz apart in the rubidium D1 line. We test these predictions by detecting photons leaking through our filtering elements after exciting our warm atoms with control field pulses (for fixed ∆). This procedure is repeated for different etalon detunings (dots in Fig. 3a). These measurements are accurately resembled (see solid blue line in Fig. 3a) by convoluting the simulated Q(∆) with the etalon transmission function exhibiting a 24 MHz bandwidth, which models our second etalon filter (dashed blue line in Fig. 3a). The etalon re(1−A)2 sponse function E(∆) = 1+R2 −2R was convolved 2π∆ cos( F SR ) with each of the cold atom response background components (dotted red line in Fig 3a) separately and then normalized individually to the input number of background photons before entering the etalon. The total response is the sum of the two convolutions (blue line in Fig. 3a). For the simulation, we have used R= 0.9955, A=2 ∗ 10−4 and a FSR= 13.6GHz. Following our previous procedure we obtain the room temperature background response QRT (∆) by considering two cold atom background responses Q1 (∆) and Q2 (∆) (corresponding to the two excited transitions of the rubidium D1 manifold, see blue dotted line in Fig. 3b) and convoluting them with the velocity distribution of the moving atoms (see Fig. 3b red line). This model is in agreement with measurements of the background with fixed etalon detunings and varying ∆. The final prediction for the room temperature SBR is calculated as SBRRT = (ηRT (∆))(TRT (∆))/(QRT (∆)) (solid red line in Fig. 3c). This final model resembles well the features of the SBR measurements, showing an optimal region of operation near a detuning of 500 MHz from the central F = 1 to F 0 = 1 resonance. The optimal performance region is probed by using a one-photon detuning ∆ ∼ 250 MHz (red detuned), and

4

6000

SBR

Integrated counts

8000

4000

6 5 4 3 2 1

0.5

2000 0

-1

1 1.5 Storage time ( µs)

0 Time (µs)

1

Integrated counts

300 200

0

0

2

|H> |V> |H>+|V> |H>−|V > |H>+i|V > |H>−i|V >

400

100

2

SBR ROI 1

2 Time (µs)

3

4

FIG. 4. Storage and retrieval of single-photon-level pulses with high signal to background ratio. (a) Storage of |Hi polarization in one rail within the optimal performance region (∆ ∼ 250 MHz) displaying a SBR ∼6 (dark blue histogram); measured optimized background (light blue histogram); original input (black dots); Inset: SBR vs. storage time (black dots, the red line is a guide to the eye). (b) storage histograms for six different input polarizations using the dual rail system, |Hi (green dots), |V i (red dots), |Di (blue dots), |Ai (purple dots), |Ri (yellow dots) and |Li (black dots), displaying an average SBR of 2.9 ±0.04 with an average efficiency of 5.1% ± 0.07 within a region of interest (ROI) of 400 ns (vertical dashed black lines).

storing light pulses with an average hni = 1 photons and |Hi polarization using only a single rail of the setup. The result shows a SBR of ∼6 for a storage time of 700 ns and a coherence of a few microseconds (see Fig. 4a). Universal qubit operation is verified by using the dual-rail setup sending in and retrieving three sets of orthogonal polarizations, where now the background is inevitably twice that of the single rail. Our outcome was an average SBR of 2.9 ±0.04 with an average efficiency of 5.1% ± 0.07 for the six polarization states |Hi, |V i, |Di, |Ai, |Ri, |Li within a region of interest (ROI) of 400 ns (equal to the input pulse width) upon switching the control field (see Fig. 4b). The polarization of each of the retrieved qubit states was evaluated using the technique presented in our previous results [23]. We use a rotating quarter wave plate and a horizontal polariser. The intensity oscillation caused by the rotation of the plate can be used to obtain the Stokes vectors of the retrieved qubit states (see Fig. 5a-

f). To evaluate the total polarization fidelity we perform the following procedure: (a) measurement of the polarization of all the input states, (b) qubit storage experiment and determination of the output Stokes vectors (Sout ), (c) rotation of input states to match the orthogonal axis of the normalized stored vectors (Sin ) (see Fig. 5g and 5h) and (d) evaluation of the total fidelity using p F = 21 (1 + Sout · Sin + (1 − Sout · Sout )(1 − Sin · Sin )). We obtained an average fidelity of 86.6 ± 0.6%. This result is well above 83.6%, the maximum fidelity achievable considering any classical strategy exploiting the nonunitary character of the memory efficiency, for a system using attenuated coherent states with hni = 1 and storage efficiency of 5% [29]. This is the first time such important boundary has been crossed with a room temperature device, rendering our system suitable for true quantum operation. Next we compare our unconditional room temperature quantum memory with qubit memory protocols using cold atoms. In Table I we list the current forefront of comparable qubit storage experiments performed with Bose Einstein condensates [30], single trapped atoms in cavities [31] and atomic frequency comb cryogenically cooled crystals [29]. TABLE I. Comparison of quantum memory systems Type η(%) τ (us) F (%) T (K) BEC [30] 24 1 100 100−9 Single atoms [31] 9.3 2 92.7 25−6 AFC crystals [29] 10 0.5 95 2.8 Atomic vapor 5 0.7 86.6 333

It is clear that our room temperature implementation still demands further improvement before attaining the performance thresholds of the cold atom counterparts. We note that decoherence times on the order of ms are possible using paraffin coated cells. Further noise reduction can be achieved by using etalons with different FSR that reduce the Stokes contribution. Most importantly, our model also shows that a decrease in the inelastic scattering rate can be engineered by applying repumping schemes. This relatively simple improvements could bring the qubit SBR to 10 and the average fidelity to 95%, already above the relevant threshold to operate quantum memories in secure quantum cryptographic systems [32]. This further suppression of the background will allow to use the memory with single-photon storage efficiencies of 15% and fidelities above 98%. This outlook makes us believe that our implementation is reaching its potential of being simultaneously effective, resource-moderate and operational in non-controlled environments, all desirable attributes of a quantum memory architecture. E. F. kindly thanks A. Neuzner, T. Latka, J. Schupp, S. Ritter and G. Rempe for performing and discussing preliminary experiments on the topic of this paper at the Max Planck Institute of Quantum Optics in Garching,

Integrated counts

Integrated counts

5 500 400 300 200 0 200

|H> Fit 50

100

150

150

300

200

200

100 0 0 300

|H>+ |V> Fit 50

100

200

100

|V> Fit

50 0

300

50

100 λ/4 angle

150

100 0 300 |H>−|V> Fit 200

50

150

100

150

100

100 0 0

|H>+i|V> Fit

50

100 λ/4 angle

150

|H>−i|V> Fit

0 0

50

100 λ/4 angle

150

Input

Efficiency(%)

SBR

Fidelity(%)

H

5.3

2.8

88.5

V

5.4

3.0

88.3

D

5.1

2.9

86.0

A

5.1

2.9

87.0

R

4.9

2.8

84.9

L

5.0

2.8

85.0

Average

5.1

2.9

86.6

FIG. 5. Unconditional quantum memory for polarization qubits. (a-f) Polarization analysis of six different retrieved qubits; the purple dots are measurements for different positions of the λ/4 plate; the red lines are Fourier transform fits from which the Stokes parameters are extracted. (g) Poincare sphere of the rotated original states Sin . (h) Poincare sphere of the retrieved states Sout . (i) table of all polarization qubits (|Hi, |V i, |Di, |Ai, |Ri, |Li) with their individual storage efficiencies, SBR’s and Fidelities.

Germany. The work was supported by the US-Navy Office of Naval Research, grant number N00141410801 and the Simons Foundation, grant number SBF241180. C. K. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada. B.

J. acknowledges financial assistance of the National Research Foundation (NRF) of South Africa. Correspondence and requests for materials should be addressed to E.F. ([email protected]).

[1] Datta, A. et al. Compact Continuous-Variable Entanglement Distillation. Physical Review Letters 108 (2012). [2] K´ om´ ar, P. et al. A quantum network of clocks. Nature Physics 10, 582–587 (2014). [3] Lvovsky, A. I., Sanders, B. C. & Tittel, W. Optical quantum memory. Nature Photonics 3, 706–714 (2009). [4] Bussi`eres, F. et al. Prospective applications of optical quantum memories. Journal of Modern Optics 60, 1519– 1537 (2013). [5] Northup, T. E. & Blatt, R. Quantum information transfer using photons. Nature Photonics 8, 356–363 (2014). [6] Reiserer, A. & Rempe, G. Cavity-based quantum networks with single atoms and optical photons. Reviews of Modern Physics 87, 1379–1418 (2015). [7] Lee, K. C. et al. Entangling Macroscopic Diamonds at Room Temperature. Science 334, 1253–1256 (2011). [8] Bader, K. et al. Room temperature quantum coherence in a potential molecular qubit. Nature Communications 5, 5304 (2014).

[9] Yao, N. et al. Scalable architecture for a room temperature solid-state quantum information processor. Nature Communications 3, 800 (2012). [10] Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015). [11] Krauter, H. et al. Deterministic quantum teleportation between distant atomic objects. Nature Physics 9, 400– 404 (2013). [12] Duan, L.-M., Lukin, M. D., Cirac, J. I. & Zoller, P. Longdistance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001). [13] Abruzzo, S., Kampermann, H. & Bruß, D. Measurementdevice-independent quantum key distribution with quantum memories. Physical Review A 89 (2014). [14] Angelakis, D. G., Das, P. & Noh, C. Probing the topological properties of the Jackiw-Rebbi model with light. Scientific Reports 4 (2014). [15] Heshami, K. et al. Quantum memories: emerging applications and recent advances. arXiv preprint

6 arXiv:1511.04018 (2015). [16] Saunders, D. J. et al. A Cavity-Enhanced RoomTemperature Broadband Raman Memory. arXiv preprint arXiv:1510.04625 (2015). [17] Ritter, R. et al. Atomic vapor spectroscopy in integrated photonic structures. arXiv preprint arXiv:1505.00611 (2015). [18] Borregaard, J. et al. Room temperature quantum memory and scalable single photon source based on motional averaging. arXiv preprint arXiv:1501.03916 (2015). [19] Eisaman, M. D. et al. Electromagnetically induced transparency with tunable single-photon pulses. Nature 438, 837–841 (2005). [20] Reim, K. F. et al. Single-Photon-Level Quantum Memory at Room Temperature. Physical Review Letters 107 (2011). [21] Hosseini, M., Campbell, G., Sparkes, B. M., Lam, P. K. & Buchler, B. C. Unconditional room-temperature quantum memory. Nature Physics 7, 794–798 (2011). [22] Sprague, M. R. et al. Broadband single-photon-level memory in a hollow-core photonic crystal fibre. Nature Photonics 8, 287–291 (2014). [23] Kupchak, C. et al. Room-Temperature Single-photon level Memory for Polarization States. Scientific Reports 5, 7658 (2015). [24] Manz, S., Fernholz, T., Schmiedmayer, J. & Pan, J.-W. Collisional decoherence during writing and reading quantum states. Physical Review A 75 (2007).

[25] Phillips, N. B., Gorshkov, A. V. & Novikova, I. Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing. Physical Review A 83 (2011). [26] Bashkansky, M., Fatemi, F. K. & Vurgaftman, I. Quantum memory in warm rubidium vapor with buffer gas. Opt. Lett., OL 37, 142–144 (2012). [27] Vurgaftman, I. & Bashkansky, M. Suppressing four-wave mixing in warm-atomic-vapor quantum memory. Physical Review A 87 (2013). [28] Lauk, N., O’Brien, C. & Fleischhauer, M. Fidelity of photon propagation in electromagnetically induced transparency in the presence of four-wave mixing. Physical Review A 88 (2013). [29] G¨ undoan, M., Ledingham, P. M., Almasi, A., Cristiani, M. & de Riedmatten, H. Quantum Storage of a Photonic Polarization Qubit in a Solid. Physical Review Letters 108 (2012). [30] Riedl, S. et al. Bose-Einstein condensate as a quantum memory for a photonic polarization qubit. Physical Review A 85 (2012). [31] Specht, H. P. et al. A single-atom quantum memory. Nature 473, 190–193 (2011). [32] Scarani, V. et al. The security of practical quantum key distribution. Reviews of Modern Physics 81, 1301–1350 (2009).