Experimental continuous-variable entanglement from a phase-difference-locked optical parametric oscillator

Abstract

We observed continuous-variable entanglement between the bright beams emitted above threshold by an ultrastable optical parametric oscillator ͑OPO͒, classically phase locked at a frequency difference of 161.827 324 0͑5͒ MHz. The amplitude-difference squeezing is −3 dB and the phase-sum one is −1.35 dB. Besides proving entanglement in a phase-locked OPO, such outstanding frequency-difference stability paves the way for transferring entanglement between different optical frequencies and densely implementing continuous-variable quantum information in the frequency domain.The nondegenerate optical parametric oscillator ͑OPO͒ is a natural source of continuous-variable-͑CV-͒ entangled electromagnetic fields ͓1͔. Below threshold, it is a phasesensitive amplifier whose quantum evolution can be described by a unitary two-mode squeeze operator ͓2͔, which, in the ideal case yields, for example, a common eigenstate of the amplitude-difference and phase-sum field quadratures. Since the amplitude and phase of a quantized field correspond exactly to the position and momentum of a mechanical quantum oscillator, this two-mode squeezed state is identical to that of the Einstein-Podolsky-Rosen ͑EPR͒ paradox ͓3͔, which has been implemented experimentally with finite squeezing ͓4͔ and used in CV quantum information ͑CVQI͒ ͓5,6͔. Above threshold, the OPO is a true oscillator rather than an amplifier and its dynamics become richer: as is well known, the phase difference of the two OPO signal beams undergoes, above threshold, an undamped diffusion process, driven by vacuum fluctuations and analogous to that of the phase of a laser beam, resulting in the Schawlow-Townes linewidth ͓7͔. There is, therefore, excess quantum noise on the phase difference of the OPO signal beams, compared to that of two independent ideal laser beams of the same power. This is a consequence of the number-phase Heisenberg uncertainty for the photon-number-correlated OPO beams. We made the first experimental measurement of this excess quantum noise, which can also be understood as a macroscopic Hong-Ou-Mandel interference experiment ͓8͔. It is, however, possible to suppress the Schawlow-Townes phasedifference drift by locking the phase difference of the signal beams of the OPO, thereby profoundly altering its natural dynamics and quantum properties. Indeed, perfect locking of the phase difference implies phase-difference squeezing, which means that the expected photon-number correlations in such a two-photon emitter are lost. This is clearly a different physical system from the standard OPO. Recently, CV entanglement was observed above threshold in standard OPO's ͓9,10͔ with unbridled Schawlow-Townes phasedifference drift. An elegant self-phase-locked type-II OPO, Corresponding author. Electronic address: opfister@virginia.edu PHYSICAL REVIEW A 74, 041804͑R͒ ͑2006͒

Experimental Realization of Three-Color Entanglement at Optical Fiber Communication and Atomic Storage Wavelengths

“…* kcpeng@sxu.edu.cn Two-color entangled optical beams at different frequency regions have been experimentally prepared by means of abovethreshold NOPOs with various pump lasers and nonlinear crystals [18][19][20][21][22]. Recent years, for satisfying the requirements of the developing QIN the generation schemes of multicolor CV entangled states via intra-cavity nonlinear processes have been theoretically proposed [24][25][26][27].…”

“…The storage and retrieve of quantum states of light are the important operations realizing QINs and have been experimentally demonstrated based on Cs and Rb atoms by several groups [13][14][15][16][17]. For developing practical CV QIN with both nodes and fiber transmission lines, it is essential to prepare multi-partite entangled states consisting of optical sub-modes at fiber transmission and atomic transition frequencies.Non-degenerate optical parametric oscillators (NOPOs) above the threshold are the most successful devices for producing two-color and multi-color CV entangled optical beams in the achieved experiments of quantum optics [18][19][20][21][22][23]. * kcpeng@sxu.edu.cn Two-color entangled optical beams at different frequency regions have been experimentally prepared by means of abovethreshold NOPOs with various pump lasers and nonlinear crystals [18][19][20][21][22].…”

“…Non-degenerate optical parametric oscillators (NOPOs) above the threshold are the most successful devices for producing two-color and multi-color CV entangled optical beams in the achieved experiments of quantum optics [18][19][20][21][22][23]. * kcpeng@sxu.edu.cn Two-color entangled optical beams at different frequency regions have been experimentally prepared by means of abovethreshold NOPOs with various pump lasers and nonlinear crystals [18][19][20][21][22].…”

Experimental observation of three-color optical quantum correlations

“…Squeezing in the intensity difference of the twin beams it produces above-threshold (signal and idler) [1] reached the record value of −9.7 dB [2]. Bipartite continuous variable (CV) entanglement in this system, which requires the observation of phase anticorrelations as well, was only demonstrated very recently [3,4,5]. The parametric process involves three fields, yet the pump field is typically treated as a classical quantity.…”

Standing-wave nonlinear optics in an integrated semiconductor microcavity

“…Furthermore, compact sources of single photons and entangled photon pairs [2], essential for quantum communications and quantum information processing, can be realized using spontaneous parametric down-converters [12,15].…”