At this stage, the tulips need to photosynthesize to store energy reserves for future growth and bloom. While they do need to experience a chilling period, this is only to trigger proper flowering, and since they have just bloomed this chilling has already occurred (by the bulb supplier) and will not be needed for this part of it's life cycle. For now, all you can do is to give it as much light as possible in a very sunny window, and water the potting mix only as needed when it starts to dry out. Bulbs are sensitive to staying too wet, so avoid keeping the potting mix evenly damp, and make sure any excess drained water is removed from a saucer (or cache pot or pot cover) right away so it doesn't over-saturate the roots. Cool temperatures, such as near a sunny window that happens to be drafty, will help prolong this growth stage and stave-off dormancy. If the leaves do start yellowing and shedding, reduce watering frequencies even further.

Once we experience milder weather in spring, the bulbs can be planted. (We do not have a specific reference point as far as temperature goes, but perhaps in April when frosts are fewer.) If they go dormant in the meantime, you can still try planting them in spring for a re-bloom next year, though tulips don't always perennialize well and sometimes only last one season regardless. Use the general rule-of-thumb for bulb planting and put them about 2-3 times deeper than the bulb's diameter. (So, a two-inch wide bulb should be planted about four to six inches beneath the soil surface.) If they are still actively growing at this point, they will go dormant as normal when the weather heats-up. Ideal site conditions for tulips are full sun (or at least 6 hours daily while the foliage is up) and excellent drainage.

Miri