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Physica E 40 (2008) 1888–1890 www.elsevier.com/locate/physe

Biphoton interference with a quantum dot source of entangled light A.J. Hudsona,, R.M. Stevensona, R.J. Younga, P. Atkinsonb, K. Cooperb, D.A. Ritchieb, A.J. Shieldsa a b

Toshiba Research Europe Limited, 208 Cambridge Science Park, Cambridge CB4 0GZ, UK Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB4 0HE, UK Available online 18 September 2007

Abstract We demonstrate optical interferometry beyond the limits imposed by the photon wavelength using ‘triggered’ entangled photon pairs from a semiconductor quantum dot. Interference fringes of the entangled biphoton state reveals a periodicity half of that obtained with the single photon, and much less than that of the pump laser. High fringe visibility indicates that biphoton interference is less sensitive to decoherence than interference of two sequential single photons. The results suggest that quantum interferometry may be possible using a semiconductor LED-like device. r 2007 Elsevier B.V. All rights reserved. PACS: 270.5290; 300.6250 Keywords: Quantum dot; Biphoton; Entanglement

Two-photon interferometry is a powerful technique employing coincident detection of pairs of photons to probe key characteristics of both classical and non-classical light. Such properties include the coherence length and the de Broglie wavelength, which determines the far-ﬁeld imaging resolution [1]. The nature of two-photon interference can be remarkably different from that of the constituent single photons. For example, higher frequency interference fringes have been observed using entangled photons generated by parametric down conversion [2–4], or by post-selected measurements using classical light [5], which is the basis of quantum imaging applications such as quantum lithography [2,6] and low-cell-damage biomedical microscopy [7]. Triggered entangled photon pair generation by quantum dots has recently been demonstrated [8,9], and here we study biphoton interference of the emission from such a device. A primary motivation is to observe fringes with ﬁner detail than is possible with the pump laser, in contrast to pairs generated by parametric down

Corresponding author. Toshiba Research Europe Limited, 208 Cambridge Science Park, Cambridge CB4 0GZ, UK. E-mail address: [email protected] (A.J. Hudson).

1386-9477/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2007.08.130

conversion. We also both determine and control the phase offset of the entangled state. A quantum dot can emit a pair of polarisation entangled photons by the radiative decay of the biexciton (XX) state provided the intermediate exciton (X) level is degenerate, as shown schematically in Fig. 1(a). For the measurements presented in this work, growth control [11] with molecular beam epitaxy was used to fabricate a dot with polarisation splitting 0.070.6 meV, which emits entangled photons. A single layer of InAs quantum dots was formed at the centre of a l GaAs cavity, with GaAs/AlAs distributed Bragg reﬂectors below (14 repeats) and above (two repeats). Apertures 2 mm in diameter were fabricated in a metal shadow mask on the sample surface in order to isolate single quantum dots. Photon pairs emitted by the source have 7674% ﬁdelity with the Bell state (|HXXHXS+|VXXVXS)/O2 and also with the equivalent Bell state (|DXXDXS+|AXXAXS)/O2, where H, V, D and A represent horizontal, vertical, diagonal and anti-diagonal linear polarisation of the XX and X photons. Biphoton interference was measured using an interferometer similar to that shown in Fig. 1(b). The phase control required to measure an interferogram is supplied by a polarisation-dependant phase delay. Both A polarised

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Fig. 1. (a) Energy level diagram for the biexciton decay cascade. (b) Schematic of biphoton interferometer.

Fig. 2. Normalised intensity for single photons (black) and biphotons (red) as a function of phase delay.

photons are delayed by phase F relative to the D polarised photons, so that output of the interferometer is (|DXXDXS+e2iF|AXXAXS)/O2. Interference of the twophoton amplitudes of |DXXDXS and |AXXAXS is achieved by measuring the projection onto the two-photon states |VXXVXS or |VXXHXS. The biphoton intensity variation with F results in an interferogram, with an expected period p, corresponding to a de Broglie wavelength of l/2, where l is the average wavelength of the single biexciton and exciton photons |AXXS and |AXS. For the single-photon input state |VS ¼ (|DS+|AS)/O2, the output from the interferometer is (|DS+eiF|AS)/O2. Measuring the intensity by the projection onto the state |VS would yield an interferogram with period 2p, corresponding to a de Broglie wavelength of l. We ﬁrst measure single-photon interference fringes from light emitted by a quantum dot. The dot is optically excited non-resonantly at a temperature of 10 K, at 632 nm with a frequency of 80 MHz. A linear polariser is inserted before the interferometer to select only vertically polarised photons. The intensity of the single exciton photon state |VXS is measured as a function of the phase delay, and normalised to the maximum. The results are shown in Fig. 2 as black points. Clear interference fringes are seen, and the intensity varies as a function of the phase delay in agreement with the ﬁt to expected sinusoidal behaviour, shown by the solid line. The period of the oscillations is determined to be 877735 nm (0.9970.03)l, approximately equal to the wavelength of the quantum dot emission of 885 nm, as expected. The linear polariser set before the interferometer was removed, so that entangled photon pairs emitted by the quantum dot could be analysed. The normalised biphoton intensity is equal to (gVV+gHH)/(gVV+gVH+gHV+gHH), where g represents the second-order correlation for

coincident detection of two photons with polarisations denoted by the subscripts. The measured normalised biphoton intensity, indicated by red points in Fig. 2, shows strong interference fringes. The difference in the period of oscillations compared to the classical single-photon case is very striking. The fringes ﬁt well to the predicted sinusoidal behaviour shown as a solid line (coefﬁcient of determination r2 ¼ 94.4%), from which we determine the period of the oscillations to be 442736 nm (0.5070.03)l. The period is equivalent to the de Broglie wavelength of the biphoton, which is in excellent agreement with the two-fold reduction from 885 to 443 nm expected for an entangled photon pair source. This technique offers a very direct way to measure the phase between the diagonal and anti-diagonal polarised components of the biphoton, which reveals the precise form of the emission wavefunction. From the ﬁt to sinusoidal behaviour, we determine the phase difference between the |DXXDXS and |AXXAXS components of the entangled state emitted by the source to be 0.0270.03l, which implies that (within error) our quantum dot is emitting the state (|HXXHXS+|VXXVXS)/O2. The fact that we can control the phase offset also means that the entangled state can be manipulated into another form. For example, a l/4 delay transforms the state (|HXXHXS+|VXXVXS)/O2 into (|HXXVXS+|VXXHXS)/ O2, and the photons are then polarisation anti-correlated in the rectilinear basis. We also report that the visibility of the biphoton interference fringes is double that obtained by a classical mixture of |HXXHXS and |VXXVXS correlated states, which we are able to produce by applying a strong in-plane magnetic ﬁeld to destroy the exciton state degeneracy [12]. This experiment is described in more detail elsewhere [10] and proves that decoherence between the superimposed

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polarisation components of the biphoton does not degrade the entangled state. In conclusion, strong biphoton interference has been observed for triggered entangled photon pairs from a quantum dot. Decoherence has little effect on the visibility, in contrast to two-photon interference of successively emitted single photons from a dot [13,14]. The phase difference between the emitted polarisation components of the biphoton is found to be zero. By manipulating this relative phase, we can create different entangled biphoton states. Ultimately, it may be possible to implement the source using a simple LED-like design [15]. Acknowledgements We would like to thank the EU projects QAP and SANDiE, the EPSRC and the QIP IRC for funding. References [1] J. Jocobson, G. Bjo¨rk, I. Chuang, Y. Yamamoto, Phys. Rev. Lett. 74 (1995) 4835. [2] E.J.S. Fonesca, C.H. Monken, S. Pa´dua, Phys. Rev. Lett. 82 (1999) 2868.

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