Mutual gaze is a powerful cue for communicating social attention and intention. A plethora of studies have demonstrated the fundamental roles of mutual gaze in establishing communicative links between humans, and enabling non-verbal communication of social attention and intention. The amount of mutual gaze between two partners regulates human-human interaction and is a sign of social engagement. This paper investigates whether implementing mutual gaze in robotic systems can achieve social effects, thus to improve human robot interaction. Based on insights from existing human face-to-face interaction studies, we implemented an interactive mutual gaze model in an embodied agent, the social robot head Furhat. We evaluated the mutual gaze prototype with 24 participants in three applications. Our results show that our mutual gaze model improves social connectedness between robots and users.