[Paper Review] Steady-state superradiance with Rydberg polaritons

Zhexuan Gong, Minghui Xu+5 more|arXiv (Cornell University)|Nov 2, 2016

Strong Light-Matter Interactions1 references3 citations

TL;DR

This paper proposes a steady-state superradiant laser that emits ultranarrow-linewidth, nonclassical light by embedding a Rydberg medium in a cavity with atoms in a narrow optical transition. The Rydberg blockade induces strong cavity nonlinearity, enabling phase synchronization of atoms and generating a Mollow triplet with an extremely sharp central peak, achieving linewidths up to 100× narrower than classical superradiant lasers while maintaining nonclassical anti-bunching.

ABSTRACT

A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth $nonclassical$ light. The cavity nonlinearity induced by the Rydberg medium strongly modifies the superradiance threshold, and leads to a Mollow triplet in the cavity output spectrum$-$this behavior can be understood as an unusual analogue of resonance fluorescence. The cavity output spectrum has an extremely sharp central peak, with a linewidth that can be far narrower than that of a classical superradiant laser. This unprecedented spectral sharpness, together with the nonclassical nature of the light, could lead to new applications in which spectrally pure $quantum$ light is desired.

Motivation & Objective

• To achieve steady-state superradiance with nonclassical, spectrally pure light for applications in quantum metrology and quantum information.
• To overcome the fundamental trade-off between cavity nonlinearity and the bad-cavity limit required for spectral narrowing in superradiant lasers.
• To demonstrate that photon blockade via a Rydberg medium enables both strong nonlinearity and phase synchronization of lasing atoms.
• To engineer a cavity output with a Mollow triplet superimposed on an ultra-sharp central peak, enabling sub-shot-noise-limited spectral performance.
• To enable new applications requiring high spectral purity and nonclassical light, such as quantum networks and sub-shot-noise spectroscopy.

Proposed method

• Utilize a Rydberg medium to induce strong photon blockade in a cavity, transforming the cavity mode into an effective two-level system that blocks multiple photon occupation.
• Leverage collective enhancement in the Rydberg medium to achieve strong nonlinearity without requiring single-atom strong coupling, preserving compatibility with the bad-cavity limit.
• Model the system using a master equation for the cavity field and atomic operators, incorporating the effective two-level nature of the blockaded cavity mode.
• Apply a cumulant expansion and adiabatic elimination to derive the steady-state cavity field correlation function and linewidth, accounting for the modified commutation relation $[b,b^{ullet}]=1-2b^{ullet}b$.
• Analyze the cavity output spectrum to identify the Mollow triplet structure and the emergence of an ultra-narrow central peak due to the blockade-induced energy scale.
• Use the effective Rabi frequency $\Omega_{\text{eff}}$ and the modified decay rate $\Gamma$ to describe the dynamics and spectral properties of the output light.

Experimental results

Research questions

• RQ1 Can steady-state superradiance and nonclassical light generation be simultaneously achieved in a cavity with a Rydberg medium?
• RQ2 How does photon blockade in a Rydberg medium modify the superradiance threshold and the linewidth of the emitted light?
• RQ3 What is the spectral structure of the cavity output, and can it exhibit a Mollow triplet with an ultra-sharp central peak?
• RQ4 Can the linewidth be parametrically reduced below the classical superradiant limit via the blockade effect?
• RQ5 What is the trade-off between spectral narrowing and power in the narrow spectral component, and how can it be mitigated?

Key findings

• The cavity output spectrum exhibits a Mollow triplet structure due to the effective two-level system formed by the Rydberg-blockaded cavity mode.
• An ultra-sharp central peak emerges in the spectrum, with a linewidth $\Gamma_{\min} = 2\tilde{\kappa}C\gamma$ that is parametrically smaller than the classical superradiant linewidth $C\gamma$.
• For $N = 10^6$ lasing atoms and $\tilde{\kappa} \ll 1$, the linewidth can be up to 100 times narrower than that of a classical superradiant laser.
• The output light is nonclassical, with clear anti-bunching observed in $g^{(2)}(t)$, due to the Rabi oscillation time required to refill the blockaded cavity after photon emission.
• The photon flux is nearly maximized at $\langle b^\dagger b \rangle \approx 1/2$, while the narrow spectral component contains a fraction of power proportional to $\langle 1 - 2b^\dagger b \rangle$.
• The linewidth reduction arises from the modified commutation relation in the blockaded cavity, which suppresses successive photon emissions and renormalizes the effective decay rate.