Some info to help you break the flea cycle ...

You must keep in mind the life cycle of the flea. From egg to larvae to
adult is between three to six weeks: to get rid of fleas in your house, you
must break this cycle. As a practical matter, this means you will almost
certainly have to repeat your efforts in several weeks to catch the fleas
from the larvae that didn't get destroyed the first time around. This is
also why it is important to address the problem of the eggs and larvae as
well as the adult fleas.

After taking a blood meal, fleas either lay eggs on your pet or in its
surrounding environment. Eggs on your pet are often shed onto its bedding or
into the carpet. A pair of fleas may produce 20,000 fleas in 3 months. Eggs
hatch after 2-12 days into larvae that feed in the environment -- generally
on digested blood from adult fleas and other food matter in their
environment. The food required at this stage is microscopic, and even clean
carpets often offer plenty of food to the larvae. The larvae are little
wiggles about 3-4 millimeters long, you may see some if you inspect your
pet's bedding carefully.

Larvae molt twice within 2-200 days and the older larvae spin a cocoon in
which they remain for one week to one year. When in this cocoon stage the
young flea is invulnerable to any kind of insecticide and to low, even
freezing, temperatures. Only sufficient warmth and the presence of a host
can cause them to emerge. This long cocooning period explains why fleas are
so difficult to eradicate.

Keeping clean

Having your carpets professionally cleaned WILL NOT get rid of the fleas,
unless they use something that is meant to kill fleas (some are very toxic
though and the reason I had to look for other means). However, regular steam
cleaning will remove much of the eggs, larvae and the food that the larvae
feeds on, so it can be useful in conjunction with other methods.