Bunching and antibunching in four wave mixing NV center in diamond

Raza, Faizan; Ahmed, Irfan; Zhang, Dan; Imran, Al; Khan, Abubakkar; Lau, Condon; Zhang,Yanpeng

Published in:AIP Advances

Published: 01/10/2018

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Published version (DOI):10.1063/1.5039979

Publication details:Raza, F., Ahmed, I., Zhang, D., Imran, A., Khan, A., Lau, C., & Zhang, Y. (2018). Bunching and antibunching infour wave mixing NV center in diamond. AIP Advances, 8(10), [105320]. https://doi.org/10.1063/1.5039979

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Bunching and antibunching in four wavemixing NV center in diamondCite as: AIP Advances 8, 105320 (2018); https://doi.org/10.1063/1.5039979Submitted: 13 May 2018 . Accepted: 08 October 2018 . Published Online: 17 October 2018

Faizan Raza, Irfan Ahmed , Dan Zhang, Al Imran, Abubakkar Khan, Condon Lau, and YanpengZhang

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AIP ADVANCES 8, 105320 (2018)

Bunching and antibunching in four wave mixingNV center in diamond

Faizan Raza,1,a Irfan Ahmed,2,3,a Dan Zhang,1 Al Imran,1 Abubakkar Khan,1Condon Lau,2,b and Yanpeng Zhang1,c1Key Laboratory for Physical Electronics and Devices of the Ministry of Education& School of Science & Shaanxi Key Lab of Information Photonic Technique,Xi’an Jiaotong University, Xi’an 710049, China2Department of Physics, City University of Hong Kong, Kowloon, Hong Kong SAR3Department of Electrical Engineering, Sukkur IBA University, 65200 Sindh, Pakistan

(Received 13 May 2018; accepted 8 October 2018; published online 17 October 2018)

The determination of classical and quantum states through photon bunching and anti-bunching like phenomena may have potential applications in quantum informationprocessing and long-distance quantum communications. We report the photon bunch-ing and multi anti-bunching like phenomena by generating multi-order fluorescenceand four-wave mixing (FWM) at room temperature using the Nitrogen-vacancy (NV)center in diamond. We have implied FWM process to demonstrate the interferencepattern emerging from NV of nano-crystals in classical, nonclassical and interme-diate (classical and nonclassical) regimes. Intersystem crossing is controlled by thefluence of incident beams. The interference pattern from dominant ionization of NV-

to NVo and NVo to NV- suggests the bunching and anti-bunching like phenomenaof photons, respectively. © 2018 Author(s). All article content, except where oth-erwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5039979

I. INTRODUCTION

Second-order coherence known as two-photon bunching led the emergence of quantum optics.1

The correlation and interference phenomena provide a solid foundation for development of quantumtheory of photons.2 Paul Dirac considered the single photon interference in which superposition onlycomes from the photon itself3 However, in the case of the generation of twin/paired photons, a similarstatement can be established for interference of two photons, in which superposition comes from thepair of photons jointly measured (analogous definition of Dirac) sharing the same energy level asin multi-wave mixing (MWM).4,5 Recently, photon bunching in the case of polarized beam splitters(PBS) has been demonstrated using diamond NV defects.6 The classical-to-quantum transition withFWM7 and classical and nonclassical bunching control by nonlinear response of the media5,8 can bedevised using FWM.

In this regard, due to stable photon emission9 with high quantum efficiency10 of nitrogen-vacancy(NV) color center, the negatively charged NV center in diamond is configured here with FWM processto realize the intersystem crossing (ISC) by changing the fluence of lasers, which can modify thenonlinear optical response of the media5,8 in nano-diamond (ND).

Multidressed suppression and enhancement of self-diffracted SP-FWM process is studied inhot atomic system including sodium hyperfine structures of the ground states.11 In rare earth dopedcrystals (Pr3+:YSO), AT-splitting caused by strong dressing effect is studied in both spectral andtemporal signal in mutli-level atomic systems.12,13 Unlike Pr3+:YSO and hot atomic systems, dressing

aFaizan Raza and Irfan Ahmed contributed equally to this workbElectronic mail: condon.lau@cityu.edu.hkcElectronic mail: ypzhang@mail.xjtu.edu.cn

2158-3226/2018/8(10)/105320/6 8, 105320-1 © Author(s) 2018

105320-2 Raza et al. AIP Advances 8, 105320 (2018)

effect in NV center is very weak. We have studied competition between SP-FWM and multi-orderfluorescence emission in hybrid signal in weak dressed atomic-like system.

In this paper, we show the classical bunching of indistinguishable photons in both two andthree modes under the phonon induced mixing state of ISC in a three level V-type system withspontaneous emission of FWM by changing the fluence of the non-resonant beam. The setting ofnon-resonant beam to high fluence is termed as high gain regime to achieve bunching like effect. Wealso demonstrate the photon multi anti-bunching like effect in the low gain of spontaneous parametricFWM (SP-FWM) by fine fluence tuning of the resonant beam and fixing the non-resonant beam. Thesetting of resonant beam and fixing the non-resonant beam is termed as precise quantum threshold toachieve anti-bunching like effect. Furthermore, we observed intermediate (classical and nonclassical)state by exciting system in medium gain regime. For the first time, we observed multi antibunchinglike effect using slow light.

II. EXPERIMENTAL SETUP AND THEORETICAL MODEL

We used two tunable dye lasers (narrow scan with a 0.04 cm−1 linewidth) pumped by an injection-locked single mode Nd:YAG laser (Continuum powerlite DLS 9010, 10 Hz repetition rate, 5 ns pulsewidth) which are used to generate the pumping fields E1 (ω1, ∆1) and E2 (ω2, ∆2) with detuning∆i =ωmn − ωi. where ωmn denotes the corresponding atomic transition frequency and ωI is thelaser frequency. The sample used in our experiment was a bulk NV center crystal, consisting ofsubstitutional nitrogen-lattice vacancy pairs orientated along the [100] crystalline direction. Thesample used in our experiment contains 0.05% nitrogen per diamond crystal. The sample held in acontainer at 77 K in a cryostat. Acquisition time of the experiment is 100ms. The NV center is knownto exist in negative (NV−) and neutral (NV0) charged states as shown in Fig. 1(e). The features ofNV− and NV0 are their optical zero phonon lines (ZPL) at 1.945eV (637nm) and 2.156eV (575nm)respectively. The NV− center is treated as a three-level system with a ground triplet state (3A), atriplet excited state (3E), and an intermediate singlet state (1A). The ground and excited energy levelof site NV0 is labeled by 2E and 2A1 respectively. In our experiment, with E1 (575nm) and E2(637nm) excitations, the hybrid signals which include SP-FWM and fourth-order fluorescence (FL)signals, are generated simultaneously. Figure 1(c) shows hybrid signals detected by D3. The sharppeak shown in fig. 1(c) comes from direct transition from

3E , ms = 0⟩

to 3A2, ms = 0

⟩with SP-FWM

signal emission. The second peak relates to intersystem crossing (ISC) by phonon assisted transitionand then decays to the ground state with fluorescence emission. In Fig. 1(c2), t1-t4 represents timeposition of boxcar gate of the hybrid signal.

By opening E1 and E2 fields, the Stokes Es and anti-Stokes Eas, are generated with phase-matching condition k1 + k2 = kas + ks. Both Es and Eas are detected pair of photomultiplier tube

FIG. 1. (a) and (b) three level system in NV center exited by two and three laser beams, respectively. (c) Time domain signalfrom the NV center, where t1-t4 are different positions of boxcar gate. (d) Experimental setup, (e) The NV0 and NV- chargestate inter-conversion mechanism.

105320-3 Raza et al. AIP Advances 8, 105320 (2018)

PMT1 and PMT3, respectively as depicted in Fig. 1(d). The FL signal generated along with SP-FWM is also detected by PMT2. The perturbation chain of Eas in a V-type three level system

is ρ(0)00

w2−−→ ρ(1)

20

ws−−→ ρ(2)

00

w1−−→ ρ(3)

10(as). The density matrix for anti-Stokes in a V-type system can bewritten as

ρ(3)as =

−iG1G2G2

(Γ20 + i∆2)(Γ00 + i(∆2 − ∆s)(Γ10 + i(∆2 − ∆s + ∆1) + d1)(1)

where d1 = |G2 |2/[(Γ12 + i(∆1 − ∆s)] is the dressing effect. Gi = µijEi/h is the Rabi frequency of Ei

with the electric dipole moment (µij) of levels |i〉 and |j〉, Γij is the transverse decay rate. Lifetimes ofanti-Stokes signal can be written asΓ= Γ10+Γ00+Γ20. The intensities of the ES and EaS are described as

δ_

I S/aS(t)= I0(S/aS)e[−ΓS/aSt] where δ_

I 0(S) ∝ρ

(3)10(S)

2

and δ_

I 0(aS) ∝ρ

(3)10(aS)

2. Now we discuss FL signal

in V-type system generated via perturbation chain ρ(0)00

w1−−→ ρ(1)

10

w∗1−−→ ρ(2)

00

w2−−→ ρ(3)

20

w∗2−−→ ρ(4)

00

w3−−→ ρ(5)

30

w3−−→

ρ(6)33 can be written as

ρ(6)33 =

|G1 |2 |G2 |

2 |G3 |2

(Γ10 + i∆1)(Γ20 + i∆2 + d∗1)(Γ00 + d∗2)(Γ20 + i∆3)Γ00Γ22(2)

Where d∗1 = |G2 |2/[(Γ00 + |G1 |

2/(Γ20 + i∆1)] and d∗2 = |G2 |2/[(Γ00 + i∆3] are the nested and cascaded

dressing effect caused the fields, respectively. The third order correlation function14 can be normalizedas

G(3)(τ1, τ2, τ3)∝ 1 + sinc2(∆ω(t1 − t2)

2

)+ sinc2

(∆ω(t2 − t3)

2

)+ sinc2

(∆ω(t3 − t1)

2

)+ 2 sinc

(∆ω(t1 − t2)

2

)sinc

(∆ω(t2 − t3)

2

)sinc

(∆ω(t3 − t1)

2

)(3)

G∗(3)(τ1, τ2)= 4(1 + α2)S1e−[Γ10τ1+Γ10(τ1+τ2)] + 2α2S2[cos(∆1τ2 + φ)e−[Γ10τ1+Γ20(τ1+τ2)]]

× 2α2S3[cos(∆1τ1 + φ)e−Γ20τ1 ] + 2R11R22R33 (4)

Where τi , τj , τk , τ1 = t1 − t2, τ2 = t2 − t3 and τ3 = t3 − t1.

III. RESULTS AND DISCUSSION

Herein, we investigated two-photon bunching and antibunching like phenomenon by changingfluence of off resonant E1 beam from 89 (mJ/cm2) to 12 (mJ/cm2). For measuring and calculatingtwo-photon bunching, we blocked the PMT3 and kept the rest of the PMTs on scanning mode.

The second order correlation function can be described as11 G(2)(τ1)=⟨δ_

I 1(t1)δ_

I 2(t2)⟩. Where

τ1 is the selected time delay and δ_

I 1/2(t1/2) are intensity fluctuations. By simplifying G(2)(τ1),two photon bunching and anti-bunching can be written as G(2)(τ1)∝ 1 + sinc2(∆ω(t1 − t2)/2) andG(2)∗ (τ1)= |Rc3RE |

2(e−2Γ+ |τ | + e−2Γ− |τ | − 2cos(Ω|τ |)e−(Γ++Γ−) |τ |) respectively. Where Rc3 and RE areconstants. By opening E1 and E2 fields, Es and Eas are generated along with FL emission in a com-posite channel. The competition between SP-FWM and FL composite signal determines the sign ofcorrelation function to be positive or negative (Fig. 2(a1)–(a6)). By changing fluence of E1 from 89(mJ/cm2) to 12 (mJ/cm2), photon bunching is switched to photon antibunching like phenomenon.In order to understand switch between classical (bunching) and nonclassical (antibunching), we usedouble dressing effect of E1 and E2 beams. Dressing effect can be used to control precise emissionof FL and SP-FWM emission in a composite signal.12 In case of single dressing field, FL signalρ(2)

11 = |G1 |2/[Γ11 + |G1 |

2/Γ11] increases gradually with increasing fluence of E1, when the fluence isfurther increased the FL signal evolves from dressing state to suppression, caused by the dressing effect|G1 |

2/Γ11 of E1. With further suppression of FL signal the SP-FWM emission is enhanced gradually athigh fluence. However, in double dressing scenario, dressing effect dependence on fluence is slightlyreversed. When E1 is at 89 (mJ/cm2), strong FL ρ(4)

22 = |G1 |2 |G2 |

2/(Γ10 + i∆1)(Γ20 + i∆2 + d11)Γ11Γ00

105320-4 Raza et al. AIP Advances 8, 105320 (2018)

FIG. 2. Measured second-order temporal correlation function (a1)-(a3) by changing the fluence of E1 (575 nm) from89 (mJ/cm2) to 12 (mJ/cm2) and fixing E2 (637 nm) at 12 (mJ/cm2). (b1)-(b3) by changing the fluence of E2 (637 nm)from 89 (mJ/cm2) to 12 (mJ/cm2) and fixing E1 (575 nm) at 12 (mJ/cm2). (c1) and (c2) Simulated second-order temporalcorrelation functions corresponding to (a1) and (b1), respectively.

(where d11 = |G2 |2/[Γ00 + |G1 |

2/(Γ10+i∆1)]) emission from substate 2A1 (NV0) results in strongphoton bunching as shown in Fig. 2(a1). Intensity of FL ρFL = ρ

(4)FL dominates overall SP-FWM

ρSP−FWM = ρ(3)S/AS in composite signal i-e ρ= ρFL + ρSP−FWM due to strong dressing effect of E1 i-e

|G2 |2/|G1 |

2 ≺ 1 as seen from the variable d11. When P1 of E1 is gradually decreased, amplitude ofphoton bunching decreases as fluence of E1 is reduced as shown in Fig. 2(a3). The photon bunchingcalculated in Figs. 2(a1)–2(a3) is the result of the dominant classical emission of FL photons due tothe fluence of the E1 beam under high gain regime under double dressed state, and hence said to beclassical bunching.8 Figure 2(c1) shows the calculated two photon bunching which corresponds toFigs. 2(a1).

In order to switch pure FL emission (classical) to pure SP-FWM emission (nonclassical)7,12

double dressing effect is used. Next, we set E1 to low threshold (12 (mJ/cm2)) and change thefluence of E2 (637nm) from 89 (mJ/cm2) to 12 (mJ/cm2), to obtain quantum threshold to excite spinstate |3A2,ms=0〉 to |3E,ms=0〉 (NV-). The curves obtained with the said experimental conditions arecalculated using G(2)

∗ (τ1) and presented in Figs. 2(b1)–2(b3). At first, E2 is set at 89 (mJ/cm2) toachieve the ionization from NVo to NV-. When E2 is at high fluence, population transfer happensfrom spin state |3A2,ms=0〉 to |3E,ms=0〉 (NV-) which leads to the prominent emission of SP-FWM.Composite channel behaves as pure SP-FWM channel due to significant increase in SP-FWM, whichcomes from strong dressing effect of E2 (|G2 |

2/(Γ12 + i(∆1 − ∆s)) mentioned in Eq. (1). As fluence ofE2 is reduced, the interference between the Stokes and anti-Stokes emission becomes dominant, andantibunching like phenomena is observed as shown in Figs. 2(b2)–2(b3). As fluence of the resonantbeam is set to 1 (mJ/cm2), the anti-bunching like effect becomes more prominent (Fig. 2(b3)) dueto decrease in dressing effect of E2. The bunching count at τ=0 is less than the side peaks and alsoless than zero. All results shown in Fig. 2(b) suggests antibunching like effect.8 This phenomenonprecisely meets that theoretical results of antibunching like effect depicted in Fig. 2(c2).

By varying fluence of E1 from 63 (mJ/cm2) to 25 (mJ/cm2) (medium gain regime), compositesignal that includes prominent FL and SP-FWM emission can be obtained. Unlike Fig. (2), wecannot observe switch between pure photon bunching to antibunching like effect in Fig. (3). Thethree photon bunching calculated in Figs. 3(a1)–3(a4) are obtained using Eq. (3), which shows thedirect relationship of off-resonant field with indistinguishable photon bunching. When P1 of E1 is 63(mJ/cm2), dominant FL emission ρ(4)

22 and weak SP-FWM emission is observed as shown in Fig. 3(a1).As the P1 of E1 decreases, the photon bunching count decreases, leading to the reduced amplitudeof Gc

(3)c(bun)(t1, t2, t3) in a positive scale. One must note that this is the minimum count achieved with

E1 is set at medium fluence and E2 at 2 (mJ/cm2). To achieve upper quantum threshold under SP-FWM configuration and emission from NV-, we fix the fluence of E1 at 12 mJ/cm2 and change E2

from 63 (mJ/cm2) to 25 (mJ/cm2). When E2 is at 63 (mJ/cm2), SP-FWM emission is enhanced in

105320-5 Raza et al. AIP Advances 8, 105320 (2018)

FIG. 3. (A) Third-order correlation function versus delayed time by changing fluence of E1 (a1) 63 (mJ/cm2) (a2) 50 (a3)3, (a4) 25 (mJ/cm2) and by fixing E2 at 25 (mJ/cm2). (B) third-order correlation function versus delayed time with changingfluence of E2 (b1) 63 (mJ/cm2), (b2) 50 (mJ/cm2) (b3) 38 (mJ/cm2), (b4) 25 (mJ/cm2) and by fixing E1 at 12 (mJ/cm2).

composite channel but still FL emission is observed. The dressing effect of E1 and E2 beams doesnot cancel each other as they both have significant contributions at medium fluence. In Figs. 3(b1)–3(b4), a small dip is observed along with dominant peaks, which can be explained from strong FLemission in composite signal when E1 is set at medium fluence. In Figs. 3(b1)–3(b4), when E2 is setat medium fluence, dip becomes more prominent than peak which suggests that antibunching-likeeffect. Although, SP-FWM ρ(3)

20 is dominant but FL emission cannot be ignored which is evidentsmall peak in Figs. 3(b1)–3(b4).

In Fig. 4, by introducing E3, photon bunching and multi antibunching like effect is observed indouble V-type system by varying boxcar gate position. The anti-Stokes signal can be written via pertur-

bation chain ρ(0)00

w1−−→ ρ(1)

10

−w1−−−→ ρ(2)

00

w2−−→ ρ(3)

20

−w2−−−→ ρ(4)

00

w3−−→ ρ(5)

20(as) as ρ(5)as =G1GsG2G3G3/d0d1d2d3d4,

which will be parametrically amplified,15,16 where d1 is the dressing effect. In Fig. 4(a), the exper-imental conditions are same as that of Fig. (2a) besides the introduction of E3. At high fluence ofE1, pure photon bunching is observed which can be explained from strong dressing effect of E1(|G2 |

2/|G1 |2 ≺ 1) mentioned in Eq. (2) and shown in Fig. 4(a1). One can notice that as boxcar gate

position is changed from t1 to t4 (Fig. 1(c)), the SP-FWM emission increases gradually in comparisonwith the FL. SP-FWM emission is enhanced when gate position is at t4. Next in order to demon-strate the multi antibunching like phenomenon, E1 beam is set at 1 (mJ/cm2). At precised quantumthreshold the influence of E3 beam becomes strong. Switch between FL emission (Fig. 4(A)) andSP-FWM (Fig. 4(B)) can be explained by nested dressing condition |G2 |

2/|G1 |2 1 (Eq. (3)). In

Figs. 4(b1)–4(b4), multi antibunching like effect is observed which can be explained from slow lighteffect of E3. By introducing E3 beam under the quantum threshold, ρ(5)

as emission along with group

FIG. 4. (A) third-order temporal correlation function detected by fixing the fluence of E1 at 89 (mJ/cm2) and by moving theposition of the boxcar gate (t1-t4). (B) third-order temporal correlation function detected by fixing the fluence of E1 at 12(mJ/cm2) and by moving the position of the boxcar gate (t1-t4).

105320-6 Raza et al. AIP Advances 8, 105320 (2018)

velocity vg =−(∂ρ(1)10 /∂∆3)∆3=0 and the trigger time t1 = S/vg of PMT1 will change, which is very

much similar to the effect of an internal delay τ1 of Eq. (4) caused by ρ(5)as .

IV. CONCLUSION

In conclusion, second order and third order photon counting has been demonstrated experimen-tally and theoretically. The four-wave mixing process was configured to demonstrate the interferencepattern. The intersystem crossing and phonon-induced mixing by changing the fluence of laser beamssuggested the photon bunching and antibunching like effect. Moreover, the shift from the classical(bunching) to the quantum (antibunching) state, has been demonstrated by controlling the quantumthreshold of SP-FWM configuration. These results have applications in designing logic gates andsolid state quantum computation.

ACKNOWLEDGMENTS

National Key R&D Program of China (2017YFA0303700); National Natural Science Foundationof China (11474228, 61605154, 11604256); Key Scientific and Technological Innovation Team ofShaanxi Province (2014KCT-10).

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